Physics-
General
Easy
Question
When a force F is applied on a block of mass m resting on a horizontal surface then there are two possibilities, either the block moves by translation or it moves by toppling. If the surface is smooth then the block always translates but on a rough surface it topples only when the torque of the applied force F is greater than the torque of mg about a point in contact with the ground. When the force F is applied the body
When the block topples about A, the normal force:
- Passes through centre of mass
- Is zero may topple about
or it may translate.
- Shifts to the right and passes through most edge containing A
- Is zero if the surface is smooth
The correct answer is: Shifts to the right and passes through most edge containing A
Related Questions to study
physics-
In the figure shown, the masses of blocks A and B have mass
and
respectively. Pulley having moment of inertia,
can rotate without friction about a fixed axis. The inner and outer radii of the pulley are a=10 cm, and b=15 cm. respectively. B is hanging with the thread wrapped around the pulley. While a lies on a rough inclined plane. Coefficient of friction being
The tensions in the threads are
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQMAAADuCAYAAAA9fGIjAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACvCSURBVHhe7Z0HfI3n+8bTf6t0aO0RO8SqPWvUqFFq1k9rU5vYu2qvxqZEi6q9VVG7QlCbiNi1VcQesVdcf9eT9xCcJGe9J+c9ub+fz/lo3nNyekSe632e+77u+/aAIAjCC0QMBEFQiBgIgqAQMRAEQSFiIAiCQsRAEASFiIEgCAoRA0EQFCIGgiAoRAwEQVCIGAiCoBAxEARBIWIgCIJCxEAQBIWIgSAIChEDQRAUIgaCIChEDARBUIgYCC7NsWPHcOPGDe0rQU9EDASHc/HiRfz2228ICAjQrtjG5s2bUblyZRw/fly7IuiJiIHgcJYvX44ECRLAy8sL69ev165aR2BgIHLnzo1kyZLh9u3b2lVBT0QMBIdz7tw5dUf38PCAt7e3usNbQ3BwMIoVK4b/+7//w6+//ornz59rzwh6ImIg6MLJkydRpkyZl4Kwbds27ZnoYYygbNmy6vvGjRsnQuBERAwE3Thx4gRKliypFnb27Nmxc+dO7RnznD179uWOwtfXF0+fPtWeEZyBiIGgK0ePHsXnn3+uFniuXLmwZ88e7ZnXYdCxRo0a6nUDBw7EkydPtGcEZyFiIOjOwYMHUahQIbXQ8+XLh/3792vPRHD58mXUr19fxQh+/PFHPHr0SHtGcCYiBoJTCAoKQt68eZUgFC5cWAkEuXnzJpo3b4733nsPXbt2xf3799V1wfmIGAhOY+/eveqoQEEoVaoUtm/fjg4dOiBevHho27atzSlE7ixEROxHxEBwKrt27UK2bNmUIHz88cf44IMP0Lp1a1y/fl17hXUwDVm+fHnMmTMH4eHh2lXBFkQMBKfDNGPmzJmVIKRPnx7+/v7aM9Zx6tQplChRAh9++CGmTJkiQUc7ETEQYoVNmza9FASmE5lWtIbz58/jyy+/VE7HUaNG4fHjx9ozgq2IGAixBncEWbJkUYJQsWJFtcAtISQkBBUqVFDZh2HDhokQOAgRAyFWWbdu3csdQtWqVXHhwgXtGfMwWGjyIzANKYFDxyFiIMQ6K1euRKZMmdQC50KnAckc165dQ506ddTrOnfujLCwMO0ZwRGIGAguwbJly5A2bVq10GvXro1Lly5pz0TAngaNGzdWz7dq1Ur5EwTHImIguAyLFy9G6tSp1YLnDoA7AcIdQIMGDdT1Ro0a2ZyGFKJHxEBwKebNm4fkyZO/FITBgwejZ8+eWL16NTZs2ICrV69qr7QcllTT8CREj4iB4FKwZHnmzJlInDixEoSUKVOqIKOt8LhRrVo1dbQQokfEQHA56CScOnWqcihSEHx8fGzKGvA40axZM/Ueffr00a4KUSFiILgkFAQ/Pz989NFHajG3adMGDx480J6NGdY5sN7h3XffVYIgmYeYETEQXBYKwsSJE5XLkILAoiZLdgh8DSsg+T316tWTzIOFiBgILs2zZ88wduxYVdDExd2lSxfcvXtXe/Zt6Ebs16+fei09C1euXNGeEWJCxEBweViANHz4cFWQxEXeo0cP3Lt3T3v2FRQCtkvja1jvEBoaqj0jWIKIgWAI2P1o6NChaofAmoS+ffu+Jgg8UnAHQSFgQ1WmEwXrEDEQDAMDiAMGDFAxBDZEGTRo0MsWaZMnT1YiwX6L7MwsWI+IgWAouBtggRLbpFEURo4cqWYrcMdQoEABHDlyRHuldTDb8O+//2pfxU1EDATDwYXbrVs3tROgF4G7hOLFi7/VaNVSKDBMXbJjUlRFUnEBEQPBkNy6dUuZkRgj4KNjx47aM9bB2QydOnVS70H7sy12Z3dBxEAwLFy4LVq0UAs5VapU+OWXX7RnLINpy169eqnvN1cpGdcQMRAMDS3HbLXOBZ0oUSI1/TkyUY1n43UGI/l9bKrC7klxHREDwfDQYdikSZOXgjB37lzlTaCduXfv3tqrXoe+BcYa2EfxzJkz2tW4jYiB4BZQEEw9DzjGndt+3vF3796tveIVHOgaP358FXTkoFchAhEDwW1gcZKpLRpTj3QjRoa7hdGjR6sdAce9maY6CRGIGAhuw507d5TzsEqVKkoQOJNh+fLlyqZMa/L8+fORJ08eZUyKagBsXEbEQHALaBhiIPHw4cOvdVDOmjUr+vfvj+rVq6umKQ8fPrRp1DsFZdWqVTF2bzYyIgaC4QkMDFTxAbZHM/Ut4KJlsRIFgQ9OebYVHi9Y90CT05o1a7Sr7oeIgWBoNm/erAaq/PTTT2+NcmeWoHTp0koMPvvsM9VD0Vq4i6B/4f3331dTpDnSzV0RMRAMC9urlylTBpMmTYrST3D8+HE1j5GCkDNnTgQEBGjPxAzfc/r06arbEr+XQ17dGREDwZDMmDFD3fXZTTkmGE/gCHgKQu7cubF161btmehh6/YkSZIge/bscaK7soiBYDXcOjOgFtXdWE/4/6ZPgD0L2D7dUo4ePap8BRQEZhTM+Q8i89dff8HT01MFIDk1Oi4gYiCYhTl7pt+YjmPfgKZNm6ogHIeY0O3H6UZ8NGzYUJl9OO6MpcQ8l+vVWIS9DZkZ+Oqrr/DPP/9oVy2H5c1MK1IQeP7ft2+f9szr8O/AtCQf1hwrjI6IgfCSXbt2qV4BtWrVwv/+9z/VVZgVfewpSLMOF/vvv/+O2bNnY86cOWqrzpbmbFpqGnbCUmCKBlN5TPVRTJj/txdWKfKzMGUYFBSkXbUeGo2KFCmiBCFfvnxvvRePEJz7mCJFCqt2Hu6AiEEchw1Dp0yZgm+++UZZeLnwGTTjMFSekzkmnUcCS+A4NOb5N23ahAULFmDMmDFqeAnHrbM60NZzNw1Dpp2JI7oYse9B/vz5lSAULFhQfWbCo4OXl5eqb/jjjz/UtbiEiEEchUeA9u3bq2g85wvQkMO7pKNHnJ89e1bl5nnU4G6B0424s6D5xxJOnz6Nb7/9Vu04HNl4hH9/BhMpCMw2LFy4UB0dEiZMaFFQ0hz82R06dMiwPRFEDOIYrNnn3Z/VesOGDcPOnTudUsfPhcIgHhca7/A1a9ZUW3L2FIgKbulpLf7hhx90mX2wY8cOlTKkIHCc2yeffKJE0dbAKMunOUmaOyIjImIQR2BrryVLlqjWXty6cxdg6d3Z0dAuTG8AdyVc6OYCjtu3b1efdcSIEVZNUrIWClLGjBmVIDBzYOsxZNGiRaqVO8WFImNERAziANy6fv/99yoKT6OOuZkDzoatzblT4BGFuxQGGk0OQgbu6CFgx2Nb6gishTEOkyBUqlTJ6mzI0qVLlRDkyJHDpiyHqyBi4ObwvM47LAePuuJ0Ifr+GazkIhw1apQKPPK/KQ7OxN/fH+nSpXspCJYWJLF4icYkZiBssTu7EiIGbgrvvFxQNOdMmzZNu+q68NjCOysXIwUhNqBwpk6dWn0GBjpjmshEAeHr06RJgxUrVmhXjYuIgRvCuy2LaygEjBO4OvQhsBEJKw/5mZnlYEozNjA5DykI9DREFVxlrCFDhgzKj2CEn7EliBi4GYzO0yDEowHvXK4Ojy4cpso7MQuBGDdgHIEdi5iWjA3+/PNPlRWgIDCt+aYgrFu3DsmTJ8enn36q+i26CyIGbgZTd1988YUhOvn8999/yuXIhc/qQhPMHnB3QOuzI9yLtsAiJW7/KQgc684uzPQ5MPVIt2XLli2dHtfQGxEDN4LOOlbnGaEBBysJKQJcVOaCdayNoCuSfQpiCwor5zFQEChMX3/9tbJYUxjcEREDN4GmHC4e5uX1gtt2ptHYZpxeBS4QFivxTy5qLlzeUWPa3jNYyPgAR6TduHFDu/o2Bw4cUF4ERuxjC1qzGRegIPDhzqXMIgZuQvfu3ZV//+7du9oVx8CsBHcavCOydqFdu3ZqFgHdiz///LMyD/FPCgGLnDp06KCKnDjpiGfvNx2GLAdmZ6IhQ4ZYZH3m3Zk+hNjqMMS/Pwu06FCkGFD0uGtxR0QM3AAuOtp2bZ1AHBWsYuR5mUE07jgYOOOijGoR86zPVmN8Hacj161bV30/3YRk/fr1amFzuAkzHpZA0xFFhmXTsQU/KyszKQjvvPOOEkRTr0V3QsTA4PAXlWdZlhM7Ci523vnpAqQRiA5GW6DDcMKECaoxKQWFaUMWBFnr/T9x4oT6O9IpGFvw58ymKnQacodAdyR3De6EiIHB4RmegThHjQhjcIwTjVlIRI99dIVElsAF07p165cTjGzZYlM8eBRhE5XYhKXcTNt6e3srI1dsdHrSExEDA8NfRp7PeaZ1xC8mhYCBQXYvcsR8AC4emonYLGXt2rVKZFgjYYsgsIKRJdCx7f3nDoHOREviHUZDxMDA0NPPc7kjYgU8m/NowIXriNQZ/QEMatJMxJQnoXmHYsBKRWt3HKbPxwCeu23PXQURA4PCBcGF5ahUItN3jBGYuv7YA5t7cNF+9913yk8QGQoXqydtqT9gIJLHF5mRqA8iBgaFMQKeof/++2/tiu1w8ZrGj9kLPxczCExFhoSEaFdfh0FECoK1W232QeSuYsCAAW4ZzY9tRAwMCo8IPj4+KtJuD9xhcHdBC7O952CahFjcw1qD6OICPC5QLNhM1Vr4PexRyMasgmMRMTAoPD/36NHDri5ADIbRD0APPpui2gOr+Hi3HzhwoEUNVLmYGZ+wtnkJPQxM7dG9KDgWEQODwjO5PfECOhW5cIsVK4Zs2bLZVTLMXQrNRMzDWwrTlgx+WttmjPEClhhz9yE4FhEDA8JtNqv9bG3nzWwBZxDQCMQ4Ad2LtlYHstMxzUT08FsD6xeYamQtgzWwBoOt1+kCFByLiIEBYVSdrcNtKZphfz9mIVhgxAXJnoisJ7A2XsDXcyfAHQGNT9bCnQm7NPOYYi0UAhqZBMciYmBAeG5mvf+xY8e0K5bBtCFNSlxIpoYdPLtzwIm1nZJpvOH72Nr3j3EFFivxqGItrFXgMUlwLCIGBoStuSgG1lTyseiI/n4u/Mhlw6xpYDDOWjHg6+1xKbKjEQerUBCshQLCqkjBsYgYGBBu7SkGlrb0ZrVguXLllDX4zRJnlifTF+Do0ueY4OwEOhQ5eMRaKCBMTQqORcTAgNAtaOnOgOd5NghhlZ1pLkFkGDcoWrSoWpzOhA1OWJbMHYu10HQkxwTHI2JgQOg6ZBCNJcJRQTMRI/y0GLN7b1S1ANwRsOuQs3v+s7U4/7+2GJ3oQmRBleBYRAwMCOcjMngX1V2VwTmW/DLSH9Mip0jwtXw/ZxUAcaITYxcMBFoLqzP5WfkQHIuIgQFhe3H6DMwV+/BOz8Ac3YCWph553KAd2Vn9/ZgaZesza7MhhHUUPPbwmCQ4FhEDg0KfwZudg69du6YyA6wPiNx6PCZoS6abkX0M9J7DyGIjbvE57s0WGGtImTIlunbtql0RHIWIgUFhOzJG4021CZxBwHQbMwO2pPzoO2DHJO4q9IJbfJqMWCEZXVfk6GDwlLUJPGYIjkXEwKAwJcjJQ1z49PezdwDP0fY0JgkMDFRxBj36+1EIOPKNxwNTsxNr4XvQJEUxYBBRcCwiBgaFqUDGDfr376+299wlOGL60MaNG5UnYejQoQ6bZsQ4Bj0OrCmwJ2vBYxA/FwuV+PcVHIuIgUFh6S+7DidIkEBtvS0pG7YUZilYXkyxoTjYw5YtW5RBiANe7A1QsjsyPxNrKySA6HhEDAwKYwaZMmVSk4BticrHBGMQLCRiRWPnzp3VscTSowNfRy8EKyMZzGSwMKYpSzFBPwLNRoxpMBUqPgPHI2JgMLjQxowZo1KHHJ7CgCHP4tY2CbEUTnLu2bOnqnJkXIL/zXoGpgfZZYmLnH+yP8GsWbPU8wxEcuQa/9tRZiYOkuUxg8NP2a5cxMDxiBgYCBqEeCTguHUajwjvwLz7WtskxFqY0mMdAe/MTF8yc0GBYLyCC59HAab7ePfm6xiMdBQsijLNdyTs8iRi4HhEDAwC7/z0AjAaH3ncOj0CPN+zbZkjZifEBAWJd+fg4GC1G+AcA+4S2P+Q1/XYobCjMoOa+/btU1+LGOiDiIEBYHCQd0Zuk83dcbk7YErQkXdjV4EZDTZfYVckEyIG+iBi4OKw0pBOQ8YIePc1B+MITLmxpyDtuu4Ep0UxiGlqxkJEDPRBxMCF4VmZQlCpUqUYh5/SRsyzO30HegUTnQ3TkqVKlVLHkMiIGOiDiIGLQpsxm3jQS2DplCNOL+JxgUNKjA5TmxRBc81PRAz0QcTABWFOnVF7timLrmeBOegHYA8DpgSNCo8ENBYxO2Gu34GIgT6IGLgYtO7S7MPGH7aaidjUhGW+tnQtjm1Onz6N+vXrK6dhVN2XRAz0QcTAhWDknA0/OLnYXlchZypwh8DCHmekHB2BaTwbHY8sdY4KEQN9EDFwEThIlGW5XAyOshebUo40Klnb/djZbN68WaVOaVqKaWSciIE+iBi4ABQCVuFZ25TEEhiJ506DzVBMph1XgjuA8ePHK1MRaw4sqX8QMdAHEYNYhtOKGSirWbOmw4XABN+XRUPM13OXEN2EZGfC+Q+MD7CWge3fLUXEQB9EDGIR3hW5SFney7Sg3rCwiV6E2rVrY/ny5dpV53PmzBklgAyS0mId2VBkCSIG+iBiEEtQCGix5bgzvYuMIsOFx205W481aNAA8+fP173voQkWV3GMPN2UDBKaiq2sRcRAH0QMYgH2/6PfnlOQeZeMDVjHQFFgtSEXZ+/evXWpbWB6cOrUqUp8KHxMm3KEuz0CJGKgDyIGToZCwC497A1gz6xC7izYS8DeLAHfY+3atWp+IQON3LrT+chR6QcPHlS+B0uCekxf0gZ9/vx5Nc5twoQJaNq0qSq3Zq9Gjm5n6jCmTIEliBjog4iBE2GzUh8fH9WQJCQkRLtqPewFyPFirENwxOIivFOzVJj+BJ7jObGJAcdixYqp4Cb9DxzBzkYq06ZNU/4FNk7loufi5MLn7AV6Gzg2jTsAWol5FHD06DYRA30QMXASXMC8Q/Kcbm3ALDI8VvA96NDjXVgPQxEFhp+X788CqdWrV2PixIlqx0ABYmdidjHq27evsk0zQ8GBLrt371YOQv79aKCyZEdhCyIG+iBi4AS4sNjGnF2B7LlLcpvNzAMzEM5OD7KJCo8kFArWC3AnwT/5tbmBrnoiYqAPIgY6w/4C3NJz62yPEGzdulVV8fHOzIUZlxEx0AcRAx3hdtnU2pvzEW2F0XcG4saOHatdiduIGOiDiIFOMEDI3QADa/YIAX0AZcuWVZWIQgQiBvogYqADbMxh6hhsqxAwMDhp0iRVaGSNVTcuIGKgDyIGDubcuXMq2s84ga1CwJgA252xis/eiUbuiIiBPogYOBCm/diU1B4hoMmHpcw0ALlilaErIGKgD4YSgyf3b+Dc4UM4czkMrhZPpxCw+o6lwrYKAVOQ/H66E/WqYHQHRAz0wUBicAv75vVEqbx5ULTZWGy94Drde2i0oRDQVGRrq3IeL+hDYMCRMQchakQM9MEwYvAsdDP6V/LC++9/iHjJc6Hd7EOw14jL8zjbcdsDhYB3ctYb8M5uC6wBoOWXxUv2ZB7iCiIG+mAQMXiE40u7IGfKvGjcoRfalk6G1FWHY49ta0+xaNEiFC5cGAUKFFCDOmyx9VIIWHlIRyALkGxh27ZtykxEa290ff+EV4gY6IMxxCDsGKbUy4APsjfGkpOXETCkPBLGz49+a07DFvf7vHnzVO6eRTmc+c9gHb329NNbCoWATUK6dOliszWYbc2ZOuRUYXMtwQXziBjogyHE4MpuP3yZ+BMU8ZkLbqIf7RiPyp7/h8zf/47jdyNeYwm8+8+ZM0e1EY/c6YcNSHle54Nn95g4deqUGnbKRh2M/lsLPwcHnfBz0EwU1+3F1iJioA+uLwZPr2B9n2JI6FkGQwNMC+8kpjXPg/c/LQe/XZdhyQafFXSzZs1SO4IVK1ZoV1/BwB8XNweXsPouKtiViMVCTP/ZcjfnwufEZAoBzUR6VB26OyIG+uDyYnD/7Bq0yBIPn2SvgWHLNsJ/7Rr8vflv+LUrhxQeHijaZw0uxjBakEIwY8YMJQTR9f7jtGPW7HOhLlmy5K07NtN9DPSxK5AtfQT4PSz3ZZ1BQECAdlWwFhEDfXBtMXj+AIdmNkLad95H4rRZ4J3FC16ZMsHLKzO8s3ohRcJ4eDdrYyw5Fhbl7sAkBFzg7MZrCezyw9fzLM825oRCwFbmffr0sUkIGFdgkJA7j6CgIO2qYAsiBvrg0mIQfisIQ0snwyfeVTHGPxiHgvarPn2BgUE4eGQf5nWtiJTvfIiKY7bjlplIIoWAHXm4sM0dDaKD8wbY6YeNO1l0xC09dw229O5j6TLThowzMN4g2IeIgT64sBg8R+iGHsj+waco3HoxrmtXI/P8+HTUyvY+3s3RHv4hj7WrEfAszvZcPBpYuiN4E7oKGzdurCzGtk45YtaBRiK+T2hoqHZVsAcRA31wWTF4dv8YJnz1CTzi50LPDTe1q29yCfNb5IGHxzsoP24HwiLFDth/jzsCtuyyB6YbGSzk9p7jyqwhODhYdQRmP0HxEDgOEQN9cGExOIGlo/ph6M9LcSyaBsC39i/FuEG94Ls4GHc1MTAJAfP4joKNPxn4s7SvAM1EFBAGG501lyCuIGKgD64dQLQBkxCsW7dOu+I4GDfgjAG2FY+uRTlFiLMD2WWYGQrBsYgY6INbiQGFgDECPYTABD0ItCDzl9FcT0N2CeZnoJdAr+7AcR0RA31wGzEwCQEHeOgNB49w/gHtyJw1YMJkJqJHQdAPEQN9cAsx4PguevytDfDZA30DHBTCxc80pGmsuL+/v/YKQS9EDPTB8GLAqT7OFgITLHhKly6d6mVAQ9LevXu1ZwQ9ETHQB8OKAV2AFIIKFSpgw4YN2lXnQe9C0aJFUaJECXVcOHHihPaMoDciBvpgWDFgyXG8ePHs9hHYAoUgd+7cyJ8/v/qltGdcmmA9Igb6YFgxoM04U6ZMGD58uFV9COyFQpA1a1bkzJkT3bt3f1m7IDgPEQN9MHTM4PDhw+qszpZjHBKqNxQCChDFYPDgwU6fMShEIGKgD4YPIHKLzmElDOLp2VqchU6enp7IkiWLciOKhyD2EDHQB8OLAeEdmgNJ2UuQcwkdDYUgefLk8PLyUuPOhNhFxEAf3EIMTLBKkbl+Njh11J2bQpAiRQp4e3s7tNZBsB0RA31wKzEgtCKzfoBNSGxtVGqCXZEoBMwc7NixQ7sqxDYiBvrgdmJAWDrM+gGOQ2c/AVv4888/1dGAXgK+n+A6iBjog1uKAblw4YLKMlSvXl3Zha2BLdQpBKx1EDOR6yFioA9uKwaE/gNfX19lV7a0eIj9D5MlS4aqVavKmDMXRcRAH1xHDJ48QNjNW7j3LOLL8Ad3EXbvjXkC4Y9x7+49PLaiu/jTp09fDk1hMdGzZ9r/wAycspQyZUrV5kzGnLkuIgb64DJi8HDHJDQqXxPd/CZhaNd6+CJfHuTOnR+VWg7H6oNnsXt2b9QuXQB5cudG3pK1MXhxEG5ZIQpbt25F5cqV0a1bN7Oj0NiHIH369OqXTFqUuTbc7bVu3Vr7SnAULiMG99f3RZFk7+K9RJlRoVU/TJw+HeO6V0fmRB8jaZaCKFOxPvpOnI05fj1RJcdHSJCpHmbttW7iMTsTc2pSgwYNXosFcOeQOXNmNURFWpTpAxvU8mdL+7a9D5aON2nSxOxz1jw4DSu6nWJcw3XEYMNgfOHpgQ9LD8KOCxE23/BrwRhUMh48khRErxWXENFA7DG2ja8Dz3fSo+3CYFhrCGa6kUVODCwyXUghyJEjh9p6Sosy/WATmFy5cqFixYrKQs6fv60PxoBKly5t9jlrHqw45b+/uEkjcCExGIQSqeOhYO/NuG7a/t87h8k1UyNpnsZYHOkIf2xuB3wWPzWazt5n01h23qX8/PyQNGlSpE2b1qEmJcE8//zzD7Jnz676TrDvw86dO21+8PtpPTf3nCWPXbt2qfdo2bKl6nztzEI3V8aFxGAgSnh+jNJDt+GaaV2GncKk6mmQIl8z/Blp/PqR2e3wWQJPNJsTaJMYcAfA+gJ6CGbPnq1dFfSE6V3OqHSladO8CfDIYa85zV1wMTFIiNJD/jEjBk2xNFJ4wKwYhF/HgYCNCL78KNpBrAwOsrsxg4nSmch5UAw4UcqWqdV6QTFgTYuIQQQGF4P9YMPyh6GHsGxkExTKUBj9Am5EKQascOzYsaMansryZ8F5mHYGrrQl/+WXX2IWg/AneHj3Nm5cv4GbN29qj1u4HXYf7jZI32XE4N7qnvgsvgfy9t6EKyYxuP0vRpdOgHcz1Mb8SF3JD05tAk+PBKgzfT8ehB3H/GHtUKtaCeRIWxJDtpqfvkRbMiPQ9evXV2PTBOdiWDG4dRBLRndBwzq1UbN6VTV/k4a0GrXqoWWXwZi+eg9CohnyYyRcRgwen1iPiYN+xKQNZ3DPdGt/eB3bpw/CgDELcTDS7vLyvqUY2WsQFgddxuPr+7F61SbsP74QrT+vhCGbrr21M+AugGPOmJuWFmWxg+Vi8Ax3rl5DmLrtPkfY5VBcjxQYenDzCq6FOSbrY5EYXFyJziU/hkeCTChVtS6aNG6AevXq4rtaX6NY9sR4L2FONBrtj8vRnU0NgsuIgd3c/APNC5XH4DfEgJFjjjlj1FjMRLFHzGLwENfO7MY8385o0Hw4tpw5hk3T+6Fu5SpoPtIf157cxqElQ9DwxZ25+ZDFOOGAu7FFYhC6Fj1KfwqPgj0QcEG7pniIS0F/oG3+DxE/YxVMPW58NXAbMXh0dfFLMTCxceNG1d+AjrXoxqEJ+hOzGDzGrYu7MKRSeiQr2gJjJkzG1Akj8F2BlPAs1hl/bloAP98+aFrcEymL+GBlpOySrVglBoVeiMFbpSqPsKplBsRPWRRDdooYuAyPri5CswLlMGxLRMxgxfJlasAJpxyJyyz2seiY8DwYI2oVQfFKzTB0/h6cv3ESE77LiRxVOmL87+tw4vRBzGlRFDlr+iLwTbfZk3u4fcc6C5qlYtCzTGJ45GyGmZv+xX/nTisn67+H92LdjL6onC0tCjaaiGDXCYXYjPuIwZUFaF6wHAZuvI7pc+ehbJnSqvBIcA0sEYPw4Emoni0N8jWZgKAXLws/NxM1M3qiQF1fbLz0GM9OL8f3hbLg60EbIzlP72L/gsGo/2UhFChYDDU7TMSOS5Fm80eDpWLwQ0VPeMRPgnSZs+OznDmUeSpbloxI+cl7+NC7FiZsv6692Ni4T8wg/BZOBh9Gj8Gj8WW58vjbCTMXBcuxRAyOTGmCbKnzovvKiGzPxTkNkSGJF+r/ekQt/pN/dUeRLCXQf/2r9vS3d83HiJ98MXnpOqz4tSOKe2VA6e7LcNUCPbBUDHqVSwaPtOXQYeAE/DZlEvz8JmLC2BH4se23KOqVDrkr+2BGoPFb5ruNGDx4+BTDR45AjaqVVdBQcC1iFoPzmPZ9AXiX6YN/rvD8fRsLm+dBmvzNsJIek+eXsObH8shWzAd/XX6Gpyr9/Bxn9+/GgZMh/OIFd7CuV2lk/KI3doXFfDS0KmZQoBv8z2rXNJ7cv4q9s5sijcfHKNxmLkyfwqi4hRjwH7Nz585iJnJhYhKD8LML0ThPFpQfsA5XX2jB85ur0Dy3J0p0WwMamJ9f3Y1BX3kjR4X2mLl5E/aeibD8PH1mMqWQZzgw9n8o+v0UnLofc0DPKjFgNsHMaI6Hp39D2XjvIUOFgQjSrhkVw4tBaGio6nXIsmSOShdck5jE4GbAGNT+qg7GaCH7R4ET8F2p6himZYeeXtiJ/hU8kbFUW8zYcQGPn5pZ7PePY3Lrehi4+oxF1axWiUG+Tlh99D4eP36kWvM/evgAd2/9h4BxNZHIIxGKd1oCByQ4YhVDi8HJkydV49M2bdrg8uVIFkXB5YhJDJ4/e4onT5+98oiEv/j6ydNXXz++i9CTwTh07haemb3pP8SJ1aPQffhfOHsn8m4haiwSg4sr0anYB/B4Pysq12uDTh180LZtW/i0aY66lYsi/aefIlPpVphzyPipa8OKwf79+5UtlGYiNqoQXBtLAoi2E44bh1di4ti5CLxseXrRIjG4vguTu9VCyRLFUazY5/j884hHsRKlUK7Kt/AZ9BsCTrlO8ZU9GFIMAgIC1Cj2n376SRqSGAQ9xeDOfzuwcNoC7LkU8bvwJCwEF67G/HthkRjEIQwnBpxnQDMR/yEF40Ax4JHO0U1kbh5dim5VyqDa950wcMRo+A7ug+5d+2LR8ZizCTNmzMCAAQNEDDQMJQYcw852V2xVJRiLLVu2IE+ePGqS9ebNm9Xuzv7HWvzavQ6K5fBGlsyZkCF9eqRPnwE5SzaH35pNZl7/6sHP06hRI1XSLsfMCAwhBmx3Pnr0aNXufNWqVdpVwUiwbJzHhBYtWqjhNj4+Pg54tEOn7j+gb/8B6g5vevTv2wtd2rcz8/pXD34GjuGbOXMmnjxxt84EtuHyYvDgwQPVmooTltlHTzAu58+fV6PqXOFx4MABHD16VKUJhQhcWgx4luvUqZMyE/EfTxAE/XBZMaBvoGnTpupcxyoxQRD0xSXFgOdLRp7btWunHIaCIOiPy4nBwYMHVZ+5H3/8UToTCYITcSkxYC6aZqIRI0bo2l//+ZOHuHfvASyreheEuIFLiAEnHDFlyNQhe9kzlRiZh9fPYs+6+fhl/M+YsmAt9p68hgdmvCtPwi7igP8iTP75xevmrcKeM7fw6LXXPcXdM9swZ1x/9OjZDxOX7sYVc28kCHGQWBcD5nhnzZpl3kz0PBy3Di9Gl4rZkCKVFz7Lmxe5s6aDZ5aSaD91G64+elWx8jgkAD/VLYA0nhmRI09e5MycBqmylscPCw/ivrbewy+tR58G1fBde19MnTYWPlXLofmUvbgreiAIsSsG9BCMHz9e7QhWrlypXX3F0xuB8C2XGB5JPscPiw/iTng4Hv0XgGG1siJ+kjIY4X8BynQaHoqFbQojcdLcaDdzH8JevC7s2Er0Kp8GCbN8A789EZOVH/gPwFfVWmHm/giTSfCYmsj//TSE3BM1EIRYEwNaQDnmjFN5aU81x/3QDej7bU00HbIKkUejnFnUAd4eH6DWr9uhlvm/k/F1hkTIXGcGQiNZ0kMCfFHko8Qo32cllPv8wt/o36wOmvQYi3lzJ6Hrd1XRduoe3JHggSDEjhhcvXpVdSbiWGyWIsfE83AeB57jyb3rOH94M0Y3LoLkKcvAd+N5tTO4saAVsiZLgqoTj73W1OLpqXVo/1l8pKvhi93aE2HH/8bEH1qifv2WGPDbZlyUokdBUDhdDC5cuKA6E9WrVw8nTpzQrsbMjePrMKxhBRTyenFs8EiKCoPWwTSl/cC4b5AhSXq0XHLh9fl3F7dhcNmE+KRkN6wVu4IgRItTxYCLv06dOmjVqpWVZqLnuHJkNUa0a4mWTWqiSK6cKFStI+btCwFv7IEjqiBdksxo99cbYnB5J3wrJsQHRTti5VsDMARBiIzTxIC1BdWqVUPPnj1tMhO9CvGF4cjiH1AsqQeSVR2F4JvhOP1LbWRImgEt/nh7ZzCozMdI+IXsDAQhJpwiBjQTcd7hyJEjrWhu8RyPb55F0O49OHzhTQPSQYyrnQEeKetg2bGHeLCqA7IlT4pqfv++FjN4cnIt2uWMh/Q1fbFLitMEIVp0F4O1a9eicuXKSggoCmwqwT9v3LihvSIqwnH9gB+q58qPGn1XR2QNTNzciN5lE8EjZ3tsOPcMCJ2BqpkSw7veLIRGapYZsmkoCn2QCOX6rHgtGyEIwtvoKgYLFixAkSJFkDlzZpQvXx5NmjRRY9EbNmyovuafS5Yswd275hpKvtgZXNqK3sU/xTvJPkePubtx5dFT3A/ZiWkdyiDZ+8lRzXc9rqhzwRUs9imMxElyosWvWxD64DGuHvgDXcqkwkeZv8HE3e7RsFIQ9EQXMaC9eOLEiciSJQvSpEmjuhTt2LEDx48fVxWJDCTy6+nTp6umJWxeQgPS24Tj5qHF6PZ1LqRMmRE5cudF7uwZkSpdXnzbbzH+jRjir3gcugWjGxVBulTpkT13HuT0SoVU2cuj95JDEE+RIMSMw8WA3YqHDh2K4sWLK4vxpk2bou1gHBgYqNphsW9BVBmGhzfP40DACsyY/Ct+X7AGO4+EIJIOvOTJnUs4+s9KzJ46BTMWr0Pg2Rt4aLbHviAIb+JQMWAb7G7duqFGjRpqkVvaaJLZhdq1a8PX19fh3XMFQbAMh4kBOxO1bNkSdevWVZOOrGXnzp0qjuDv769dEQTBmThEDLj46Shk59tLly5pV61n3LhxaNy4sbIrC4LgXOwWA9YWsGFply5d7J6Ww6wCdwerV69WQUhBEJyHXWLAakNmA1h9+GZDEluZMGGC6mlvPt0oCIJe2CwGK1asUHdxbu0dCXvrlypVSvW2FwTBedgkBrNnz8aXX36pZtXpAUde+/n5OWy3IQhCzFgtBtzGc0ewbNky7YrjYfuzDh064N6910zIgiDoiMVi8OzZMwwbNgy1atXCrl27tKv6sG3bNpVVkBl4guA8LBIDti3v3r07ChUqpOoLuIWnxXjUqFEOf/B9OVLN29sbgwYNwpgxY8y+Th72P1g8xp9vUFCQ9i8txGViFAMKAScbNWjQQI3TnjRpEgYPHowhQ4bo8qCVuW/fvmpCLv/kbsTc6+Rh/4P/jvz5WtJ6TnB/YhQDFhBRBE6fPq2+5jmeNmO9HvQqcODqxYsX1Z/82tzr5OGYB3++chwTSIxiIOYfQYgbWBxAFATBvRExEARBIWIgCIJCxEAQBIWIgSAIChEDQRAUIgaCIChEDARBUIgYCIKgEDEQBEEhYiAIgkLEQBAEhYiBIAgKEQNBEBQiBoIgKEQMBEFQiBgIgqAQMRAEQSFiIAiCQsRAEASFiIEgCAoRA0EQFCIGgiAoRAwEQVCIGAiCoBAxEARBIWIgCMILgP8H2aBhKmtDtrwAAAAASUVORK5CYII=)
In the figure shown, the masses of blocks A and B have mass
and
respectively. Pulley having moment of inertia,
can rotate without friction about a fixed axis. The inner and outer radii of the pulley are a=10 cm, and b=15 cm. respectively. B is hanging with the thread wrapped around the pulley. While a lies on a rough inclined plane. Coefficient of friction being
The tensions in the threads are
![](data:image/png;base64,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)
physics-General
physics-
An uniform block of mass M, height h and base width a is kept on a rough inclined plane as shown in figure. Friction is enough to prevent any slipping between inclined plane and block. The angle of inclined plane is then increased. Determine the limiting value of
so that the block does not tip over ?
![](data:image/png;base64,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)
An uniform block of mass M, height h and base width a is kept on a rough inclined plane as shown in figure. Friction is enough to prevent any slipping between inclined plane and block. The angle of inclined plane is then increased. Determine the limiting value of
so that the block does not tip over ?
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of radius R, specific gravity 3 and mass ' M ' is immersed in water and fixed at the top point 'p' on its rim as shown in the fig. If can rotate in the plane of the fig about the axis passing through ' P ' If the disc is displaced by a small angle
from the vertical position what is net torque that acts on the disc about point P.
![](data:image/png;base64,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)
A uniform disc of radius R, specific gravity 3 and mass ' M ' is immersed in water and fixed at the top point 'p' on its rim as shown in the fig. If can rotate in the plane of the fig about the axis passing through ' P ' If the disc is displaced by a small angle
from the vertical position what is net torque that acts on the disc about point P.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAR0AAACXCAYAAAAoNo9xAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AADTFSURBVHhe7Z0HnF1F9ccTaYaSIMUQEIPY6CjdUA2hhRIkCEqTYkBKRHrvhCIQEDWhJSGFFkrooYQICij8kRIVpFcTQQgQShCC57/fyf7CYZj73n27m7dvkzmfz+z87pzfnDu3vLPTbyfLkiVLljpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKdjpZsmSpq2SnkyVLlrpKTU7n008/tRkzZoSQwsQex3qPY67H1bix3uO25MZ6j2NuEa6V60OKG6cVcVN5lB7rUmlKr4SL0spyhWOO0nQchxRPIebFukrY54v1cbpPK0ovo/c4TvOhpdxGlJqczv3332+nnHKKnX766fbrX//aTjvtNDvjjDMCPvXUU+2ss84KAUwaOnGJOT777LODnlhc8KBBgwq5ssv5SCuyi76IC/ZccIpLOaT3WFzhlF3pPZZd5cMmxz7fmWeeOUvPMRzP9Vh68sSYIOz10inEaT5/UUidX2lFWNyiaxE3dd3CRfcIzD0UN/UciHUO6T1GT9B7I7t6r1J29T5yrPfGl4E0caWnDMLY0jk8N7aLXnbB6GMudsGeyznEJVx22WUN53xqcjqTJ0+2v/zlL/bQQw/ZI488EuKHH354Fv6///u/EKRH5/Vg6T2XGF2crxJXesVe73HMFa6Fq7gM19v1+VLcorSyuGxQnlrypvJUw7VyPY71wrU8p7bggsu+gzFX73kRV7gSV7iM3RTX6zmeNGmS/e9//2v+BTeG5D6dLFmy1FWy08mSJUtdJTudLO0qn05/1e4ZO9KGDR9uw4ZdFvogCMOGDbcRl4+yq6+72e5/4kX7sLFaCFlaIS1yOtOnT7err77arrjiCrvyyitt9OjR4Zh4zJgxszC6q666KmBiz4XnudjyXI6FW8KVnnPqvJW4xOjEJebY6z2WXWFxhWWrkr41odo5PSaO8fXXX2+333673XzzzTZu3Lhwb4cNG2aXXHKJ/f73v7fzzz//cx2UdFyec8459rvf/c4uvvjiwBs1apRde+21IT+2brnlFrvpppvsmmuuCfdQZfD30z+Hq65uekYXHW5rfnVBm2+++W3BBRe0Bbt0sS5NIeCmsMgii9giiy1lK6+/nR19fpMTuuYqu+rKmc+f8+t6sKv3Sljnjblg9CpP/F6luLFduGD05FE+z/X3IcVFrzIUcVWGIi4YPbwiu7L10ksvNf+C21da7HRuvPHG8MLx8hLfcMMNIRYeO3Zs0AkTcywM77rrrivFhee54Fif4qp8BJULnTCxx54rrHPJrk+L9coXc4UV/HHMU0il+XTlT52TNI+5PjAO4Z577gkO4sILL7Sf//zntuOOO9rmm29uP/zhD613797Wq1cvW2ONNex73/uerbXWWrb22mvbOuusE+Lvf//7ttpqqwU9mPRNN93U+vfvbwcccIDtt99+dsQRRwT7t912W3BGnJtnw/kJ/jkRXzPsCFv5y52s04Lfsl8cd5795oLBdsEFFwSnd+45v7azTzvGdum9si3QqZN1XmxtO+z8MXbjuM/eldgu10vg3KTNOk/Tj89z0RdxY7vo0cVcYfL4MqBTvhRX55DdlnApC+cUF1zN7quvvtr8C25fyc2ruUjeeeed8B/xl7/8pW2zzTa2yiqr2Morr2xLL710qF1sueWWoRbz2GOP2ZtvvmnTpk2bFcj7+uuv27PPPmuPPvqoPfjggzZkyBBbc801rVOTQyDMO++8wQ6Oh1HOMvLxlButb7em/Mv9yO58oTkxlul/syM3XarpHF+23YZOak7M0lElO525QJ555hk78sgjbaONNrLtttsuzAMZP358cCCvvPKK/eMf/whNgj333NO22mor23777UNtA2eTEoZgL7roomBrl112CU0vajZ/+MMfQo2CWs/GG28c7FDF/+9//9uc84vy0eRxthVOp2c/u/2Zj5tTY3nbLt57pnPb/KS7m9OydFQp7XRSsyBjXE3vcS1cj9uSW01fhIv0Ps1zq/F9qIVbKSBvvfVW6JdZd911bY899rA777zT3njjjaBLydtvv21///vfQ58CNSEcB07jvffeC3qczQMPPBB0ffr0CVX6VJX9k08+CY6OJtyGG24YnA8TSz/+eKZTURk/bbI37aVrbYtmp3PT398Pes4Twqcz7KP337EpD4+2fivMZ53m62nHjHt51n0pulden+L6kNJXw8Qex3qPa+VW0ntcTa972IhSyulwEXRG8d+N6vfQoUPDCAMxx2Cq2pdeemnoYASThk56zwWnuNj3XDhgeATlQ+dxNa70Kr8wMVzhFBe9Yo/F9ThO83liXYx9iPNTFqUJ+/JxrcKkjxw5MqTRD7P44ouHvhvuK7UZOovByifMNaOnw5E+gBEjRtgOO+xg3bp1sy222CLkO+GEE2yJJZYIfT10NvNOXH755TZ8+PBZ9173FFvomSGL41l44YVDOeiL0DWMaCrneacMsNW6NDmdbt+yPv33sl8edIDtu+++Iew3YC/rv2Uv+wZOqamWs9jKW9ugi0fasMtmPmv/rlA+Xwa9VxyTLj3nJh19Ja7uL7iIC5ZdcbkvYLjgFFfn8HZr5RIXcVWGv/3tb82/4MaSUk6H/1x0QDI6ceutt4ZAZyEx1WoCOnUgChdx43w+3XNT+crajbkpfQqn0lK4tXmK9EVcrsVj6VP3AMex/PLL20477RSaUXfffXeICfDvuuuukEbguU6YMCHocAi8xEyvp3lFjQfuZpttZl/72tfsW9/6Vvhh3HvvvaEppTIR6zkKS3fHHXfYn/70p/BDWG655ewXv/hFOBc64rGXHW3r4FQ6z29fWbK7Ld1jKevevXsIPZZuOudKazQ5o73tpMHDbexNt9mEu+4IeeN3DFtFZQCjj7noy3JrsVtvLjjmMir5wgtFnWTtK7lPZw4UahjUTj744IPmlM8LVXD6cmgeHX/88fazn/0sjEDRbCLf1ltvHTqV6d/56U9/GmpMdBKTRgcyncotEWo/jJS9//7MZlSQqbfbNos1OZ0eve2i2yfZs03NsqeffjqEZ555zl58ZbK9Pb2Zm2WOkOx05kChQ5iahRecDDWZQw45xPr27Wvrrbde6GuhyURTiikQ9NfwY4fLnA6q56zh2XbbbYPT2X///UOth2F1ml6HH354cCSMduHIqgl9DAzNM3wr+eDV623L5tGru15sTswyR0t2OnOQ8MNnkd8GG2wQ+lkQmlA4Bzp+cRiMYlHDwbGUEZpR9OEwSQ8HhDDaxeQzhsYZweJ8dFRTta8mlIE+I8mHr90w0+n03M5ufSpXaeYGyU6ngwvtdvpecCw0i2geffe73w1NJrY2oGZx0EEHhXZ+UXMrJaxUpjMXh0Nn8XnnnRc6hJ977rlmxmdCTeekk06y9ddfP0w2ZBJiauSE0TM4L774WZVm+mvX22YLNjmdZba2W576qDk1y5wspZwOo1dMKqPHnN5xOhN5EXVM9ZyedGL+wwrDK+LCI5BOmuwqHzow+mpc2Y25xOKCxRUWVxid9B57fSVupZDKU2QH7M9DHw1NI54BHb3HHXdcaN7QzGFy36qrrhpmB//oRz8Kzaejjz7avvnNb4Zw4oknhpmq1G5oCmEXezgq5tRgl+dDc4z5O9RYcFTf+c53wszjww47LPC4n8zzwaFRw6GJRG2HkTJqLpSNphqO6dvf/nYYpj/44IPDKApOCNuUc9dddw3XRSDvb8880NZedEHr8vUNbP+TfmdXjhkVzkU59UyJPeaeCMPjWO8Ydkn37yPp6OESwHoHq3Glb61dMHrylOXWYjfmck+Y/tCIUsrpUG1nhIPecXrMidWLXqlH3XOV13M9rsQFe32MxVW+avpq3JYGb7NaqMRV+Wga0c+CgzjqqKPCMgV+uCxB+PGPfxx+5MyjYaQC7n333ReaQ8yJ4ceOk/jBD34Q5uowgvTnP/852MMJnHvuuaGPpl+/fsFBsOyBJQ709wwcODCMgGETezSbCBMnTgx5vvGNb4QaFcPKnIt3g3LDZWSL8uKYWCKB7QEDBoQh85VWWimMZlEGRsW4Tso+nuttyn/zzbc06WeO2mBPIzHwCGDS0AkTw8cutnT/gl3HRS+7YG835nq74NguMcfKBy/mChOLqzIQfHljri9vNW6RXXAevcpSszC5D+dBhy8/YH68OAOWKJSRl19+OTgQ+lzkoJiwt/fee4daEf0x++yzTxgi50Vlk7YywggWo13UiNgFrygf/3lxNsyxYbidphc1HWpctTT1ssxZkp1OAwodtTShcBaMHFFdTvWllBWaMV/96ldtvvnmCw6AphhV83/961/NjJYJ/2lxYPTVUBtmRjO1IxwcTpLakFalU+OiufWb3/wm9D1tsskmwdmV7dDOMudIdjoNJE8++WToQ+EHSQ2FpktbTWVnbgw/cPpefvWrX4U+IfpvTj755ODUaDqxdIHa0ZQpU2zq1Klh7RX5CCyFePfdd+0///lPcFYsf6D6Ts2L/poDDzwwzOuh9kTTCkfk5+PQtKPpRoc0tmmSMbSv2lKjbLuQZfZLRafDQj0/85T2ojAvFTHHpINpZ6qtWZardqg/RxFXeo+LuLHdWsoAFxxzhctwCeIKx1yO+THShqfzt2vXrqEZQg0APY6AH6fKLrsqr7dLHJcBDBc9tniWxPTpUPtgWQIT/6gFLbDAArbQQgvZsssuG/pe6KRmeFuTBKm14CBYVU4nM8sr5p9//lBmOo5xKNTO6HTmvMx05ly6ZjBLIshH/xTHXDeTE0ljtjLOBz7NN/p8uA5s+Xvm74P0Hsdcj2vhxufwXGJ0MdfrY670MRa3CMdpKZ0Cz5r+sjJzptpTKjod9s2ht33w4MGh45H+APY54b/Vb3/72xBzTDp6qs4EcclXjcvGUOhTXHBsl7S4DORNcYvKW80uTYIUV2X3XDDnr2SXJQWei47RB5ohK6ywgn3pS18KfSys1mbUAR6jVHD9tWGHvNwzysKxzoH9mAsHLnkoH+mMUqGDx7PVeh2cEDbg8ONnCJzyHXvssSHgHAh8DQTnQec094m8dCgTY5tzEuv+6Z4RwyMfSyHQUS7KgB3SqeFxLxg1o9zcA3S6D9jAru4Ddv21oY+5Ok8lLumeCybmPOCYS+y58AjSo0txhaUnj46FFcdc6VJ6Be4ZnfiMNjey5OZVOwmjPNQgdt5551Cb+fDDD5s1c6/QfGPTKZZjMDrXqAsWs7ROstOps9AnQm2B+SzULrJ8UT766KNQ62PInxrC59ZqZenwUpPTef7550M7lfY2bXatVhbmPzZBenSxvhJXuBoXLLvElbjeLlj5ytgt4opXhksa/RfMk2GomBm5rKCmWs68GoK3K9uKPZY+LkMlrsc+rRLX62NdCnt+SzCxMPdL94Vm3aKLLhr6leiH4h5yL+P8yqc0Qnw//XOK9S3lgj0XXA8u/V7VuDpmB8dG21enJqfD2hvajvz3oS+AWP0PtDVpyxNIJw0d7WFxaZ+TDk5xwXDJ47lggrhg2RVX56hUBmKVtzVcYnHRey7Yl5e5KqTTX0FHLfsI049Bnw55xCUfdj2WXZ3Pc4lJU7rHvgxKly5OU3oK61hpMfac+JwqcwqLK0wsG+JyrH2BfvKTn4RN2ml2qQ9Jz4w88P29x4b0shtz0Yurd1fc+PmjRycsLjj1rqTsglUGQsouMcfY4BrF5RyyK26qDN6u7iGji43WsZybV7NZmLty6KGHhpGgsvsGZ/miMHmRnQzp5GaAI0vHlZqcDhPUNLRI1Y1YzS0wsYZvwQzvEaT3XHgxN2UXvbg6h4YiK9ktwwXHXJWXuMgucTUuw75cCxP8llpqqfCfiuFM5SVWPtnydlP6SrgMt9ZQi81KXH8tZa9bmPvJffzjH/8Y5hSxkyEzm+mIp7klW6lzVLJbiatnKkwZxC16/sK8rykuuJpd0jhO/X5kV1jcSnYJvIcdunnFnBLmkDC8SRWOmOFHYYbxCAypkoYu5tI8q8Zl6E9DmOjFlT5lV9hzyR/b9WXgHOIScwxHes/1donRiSu7pIOp1jLxjSYBozBUe3E6Ko+4KoPOS5rH4irNc4m9PsbiFul9qMarRU+Iy+evRfdI3Ph+xlzdI+4d95B7yUZgzK5mZb3eBz0nuMpHrHP451SNW+ld0ftYxEVfxFUZCOSLueg5Fq7ETZVB50BPeQg0UXPzai4QZuoy1Z+Hn6XthXkozKrefffdW7yLYZb2k4pOh/4I1gExPf+f//xniJ966qkQSCcN7PVFXOFq3Bh7bkofY3Gr2fXcIr3HZbg4G0YU2FKC/Wxee+21sFwgxfW2PI71HhdxUyGVPxWKeClcRl8PLs189vCh6cpo4BNPPBE+p+O5tbxXtbwrnpvKV2S3Ndyi30/MJebedOjJgWzkxIfZ6Ag95phjwl4t7DzHNHb+0zB1nyou6ejhcVzEZU0OHDBrjAhguOjggokrcWW3GlflEZd84pImLpg0lUF6z8VOzMWe9MzgZSkA/Tds/cDCSpYHsMaJtUnM7iW/yiCMXYIwOoJwrI/TU2myobRK2OeJ0+LyUWaPieHrvoireyQuWFzdL/IoXyUuzxGd56LjfrKAlOUZPXr0CJvQ8wzErfT8wd6uf3dJ13sFvwwXnrjo0cFJ/Sa83Wpc2fW/tUp2OWbjtkafaJqbV20kTPpjS1Da1fz30ZcvWdFNm5taY5a2FyYSstKdDeT5akmWxpfsdNpAWI3NcgYWUOrFp8rPZ1twPITVV189dIRm59P2wgp45vBQ88nS+FLR6dBHoS0t9SF2tr4UJmYbTDBfE4DHNpbSo9NH3bVlpvLBlV3iFNfrhWO7pMmuyhBzheMyUFaVlzzeri8DGJ7sEnPMLFlWSuNwWB3OFhEMZ5KPFb/895XTIbCYke0+GfqlrKz6Jj+2dA7yEpTmMbE4MTfGtaT59DhNOFU+YX+PYm4qn9L8/RRXmCA9XEKKS8wQMSM5rJanO4Ch49T7CDe2C465sguXfOiLuLKr8lTigsWtZBfs7ZblUl6G3/Ul1UaVik6H/VWYAcrsWXadY+MnhuDYYxdMzLH0xOzRKlwrl1DE9Vh2fT7psUnw+hSXtLJc4hSXh80mWzgcZogy+1NcykJgOwjveBT4UibT+xkC5oVhiYTOKRsxVhlivUK1tBT2af66vZ5QdF+EdT+FpU/lE5cQP1O9Y+LqmQoTqzz+XWG/ZoaL+cggnfj8KGWXfJ4LTtlNcaUXl+cUc8EqTxm7lbgci0s+grjgSnZJ452s9O34RpDcvGqF8FUDRlAYsSoSRlXYviLleJhrgtPiB5KlbYTaJs48D6U3rlR1Onxw/5FHHrFHH33UHn/88TBUSQCT5nGsr4YrhbK8MkG2iFN2fRpY10WIr4tAfw3Dk0xSY2NzhjSVL7ZFbZFRhZTTUZhnnnnCdp6st/nrX/9qkyZNKry3wpX0lA9MAIsrDJfAueJ8nis9wdttSy7Yc/2118IVhsfGZHQu06Gvc8dc2dU5iDluFC7Yc8GV7MIThy1BGm0WspeqToePtzFcx3DkqaeeGvojCB6zVQN64iK9Ys+pFMryfEiVyWOdP3Ut4oL5bIv0YIa8wcrHMWupGBrXMCV2Yy6YdPLQkZxyOHw5U5gP2vHFB7Z1YEiYfCoPa45kF0waxxqOFxdcjUscc3WOSlywt0vMMRg9PJ/P2xVX+lR5Y27KrucOGjToc1zSuHd0KDNdga1TmUGf4sZ2ifUMU1x0MVflmZ1cQi1cAv1bjOo1quTmVQuECVj8N6XTuKywLQh9P3IwnTt3DjHzepjCTlucTvvWbMCe5TOhmcXK/tzMajzJTqcFQu2G7z/VKow2sBcxzob9hfmkDMPsjLjkT7K0rdC8YAtYOpezNJaUdjpMraYfg/YiXw5sTcAG/SAEby9lO9aTx2PpU7bamkv/DKt4e/bsGUYZOC7iChPrmKDRLJwPC0OZ9c2ne6k5sWqaLy34/LJRZNfrY67Xp7g8T/oDZBcsLljPu625YM8lJk3pHsd2y3KpMdIE4SOC7ANF/w48X16wz1dU3rbkeuy5pHmusNfXwiXmHI04L6y00+E/Me3FQw+dOU1d07k9JiYw1VxpYPqEiMWhpiCuMDqw52rqt+cy7VtcMDHHwjHXY2JsgzWtnnNwTZ7LjnUxFx5fO+BLCLzI4sRcbGFHWHaxQVue2s3Xv/714Hio5ZCGnv/KrEqnSUA7nXNhV+cosgtWGQjkEze+NnAlu5qan+J6u6ky1MItKm8Zrp5biuvLwCbyfMOdGeHsw5O6Np6ZL4Peo9guZdA7pzJwrPsHV/eaNG835sLTOWIuMef0XG/Xl4E4tisu9tFzzfTJNprk5lUNwn8mFhg+/fTTzSktE3Z1W3HFFb+wRoY9k6nxMBckS9sIk+WY1lD2q6hZZr9kp1OD8N+D7UZbKzgbmmaptULMZOZb5fynbvTVwh1BuMcskcib4DeOZKdTUl5//fXwBQem3M9uYb4FX0JgZm1eq9V6Yf4TkzAb/SN0c4tkp1NSmGbPd6rq5QTYh6d///7hnMxqztJyYV8jJl+y82WW9pfsdEoIC+jYpY6JZvUUOu/ZS2W99dYLewJnabkwLYHmcZb2l6pOhyFdesuZ/chMTc0kFWZYkhmRYGKP0QmnuF4PTunjoPQ4T1GacNE5hTXbU1h6rpMRBS0kZAtS8sRc4fgeya5wzEUnHHM5F5gh9WWWWcb22GOP4PiYTOi5muEqu8yQll3NluZYWFzy+TJg23OlF9fbFZfr9FyVJ8X1drFZjQsWt1IZYq63yzF69qxeddVVw2gP91VclUdc7DGrWc/Y201x0et5VyqDL28Rl7iIC05xwejhic8WKo286LOq02FzKuY5aF0HazxSAX3ZtFq4cZpPL9ITtC6FIKzyx/kqcZnzwAQzqud8zYG5EOKi1/oZsM+fwp4rjM5jlYc0MOej05mOUJZdsF0GczAInksszLoclcev4dG6HXFZU0dchttSu8pXxm5LuSpPEZf5KvoyBzOVmbNTyS782K4vj+eCU1zsch9q4RJ7LrHH4oJjruySRvk79NqrLBb+e/DR//YWvpvFDyfPYK5d+M/PR/v4+GGW9pXsdKoIH3ZrpJeVNVx8aYLJhGyylqW8MLmVCZlZ2ley06kiU6ZMCbULqrNtJTP+O93enzbNpr33Xthq04f333/fPvhwun1SoXb87rvvhvlCvXr1yiMyNQi77DF0TpdBlvaT7HSqCH0nLE1oS3ls7CDrv3kf23yLLcOePD5ssWVf226Hne3nvzrRLr72Xnv1veZMCWHtFg6RLU+zVBdmlG+//fb28ssvN6dkaQ8p7XRoZtArTk85XzzQFwU9JvY41gszekDMFwiF0YFJE9frlU9fNRQm5hjMqIO44LJcrslz/VcU99prrzDqgZ7gudgQV3bRYzPNvdDOO/ck27vvamHtVQidO8/a5oI9lGelh7Cgrb3dAPvtxRfZ2Wd93q6+drnGGmtYly5dwqgMX50gTdcGl9ETYl2nyqvr8+WNufpaZK1ccCWuL4Pn6hzEPPsUV9cmLnaLuKTpuRCzVw7r3tjgC4ctrmyJ68sLRo/Ol4Fj0sX1ZSjipsorLpjYc+EVcWO7nss54FE2/mk2mpR2OnTE8W1kPmTPf1am6xN7TCzMXjMeiytcjctxWa4wZSP2WFxmEosLLsulD4DNoDwXPVzhSna/yB1rJ+3eKziV7+16ht3/wANhVIxvdRP/6U9/tHv/MNHuvuYC67fizG0wNhl4oY2L7ApPnDgx7M3MQlTWc7HfMuuNOCd6No8nrlTelnBVhmpcYeLZwS1bBl3bKqusEubrsHl7Nbu6zkp2K3E5R1mucCUuOnHL2OWaX3nlleZfcONIbl5VEeZCsA6qLeX2k7cNzmTDY+9qTknJDLv+0HUCr8/pf2xOKxaGgfluOv/F6RfKkhYmebKJeZb2k+x0qgibdVHNbjv50G44rm9wJhsdX7yh+zv/HG8/X3exJt7Ctt/IJ5pcUHVhP2smMLJGjPk9Wb4oBxxwQJhQl6X9JDudKkLziv6TtpMmp3P8NjZ/k9P52ga72aAzZs4sPf30QU3t8bPsrDNOs2MPHWC9V+ne5HC+bOvufr49NbX87FL2xmU/Ffb8oZnVavlkqj028QYbMvgMO/6Yo+yoo4+3QecNsXH3TrJ3O+AieJaVtHXNNUttkp1OFWH6PJ2ObSdNTueE7WzhJqfTef6FrFu3bk2hqy2ycBebtymNGlCnBbrbBj8+2C6+/j6b/F7LVkYPGTIkdICntnQoN7Hwv/bYuMG24/rftR5LLmZdu3azxZfsbksu8RVbZKGFrOtiS9n3th5o1/713838jiH059DpnqX9JDudKsJ8GKbOt6WMP61fcC4/OOTaUDMhTP/gTXv0lotst17LWpcFlrH+x4y215v5LRUWibJFBjOq2VeGrVDZqY6V69Suijctn24TLtjTlltgXvtKz1522OBr7ckp0+zjT2bYjE8+tv88+4Bd+MutbckunazLCtvamMc6zubn7LbH/cjSflKT0+E/pHrL6RlXb7ow6epVJ0298bVwmcBVT65wiktg9i9NrDYpQxO+ffyNdmS/VW2eTp3t2zucEppAjAqyNuiOO++yK88daCt+mRrPwrbhbifZ7Xfebbfd+nm7jFJ4uzpvjLHLEGrXrl1tt912C/ON+MDfkksuGZzerrvu+rmRjltvvc1uvuUmu3Ho4fadrk1lmKe77XTCMJvQVDZGYtgfemZ577Q/jL/Cfrb2osHOEpsMtBHXjWsq1+fLQFnBKm/qnsRcpXkuscqoERrhmBvb/ezaZmI621m/5p9xzNU5KtlVGYTLliHF9Xqw9J5L7LnCShfXp4nXaCNYNTkdZsyyHIAqO5/RvfTSS8MGSVTlSR86dGgIpKNHRy3Bc8FFXDBNmSIuOMVVecpwY7sqO2nY8Vw+18oMVr4YyXWQ19sVhqvrJA1dXIaZ+CIbc9UltucGy9kCTU6nR+8D7ZJh8GdyhwwZapePucqG/Xp/W+OrM+furLTNgXb20OE2esSwWdfGp54pN3Y5N+fg/HEZ4DCcDmbBKvb4DA6Y70LhjJjXgw24w0aMseHnH20/Xof+pE7Wa/fjbfRVV9iw5nPAm2l3qI0YNcZ+d97Zdupxx9rJZ55vg3/DPfusDJ9xZ97fSuUty5W+pXZ5nptuumlwOjxrb5dYXPJxnzmWXvyYKxxzCcKVuGBxvV75YkxQ2VJpniubTz31VPMvuDGk5uaVVq/6VaypFa1F+o7GZZLVgQce2Hw0U1pul78f2vXHbGWdm37UPzjsxpAu+Yz7kT088mBbbt5O1rnb9+3km56ZmVxwrjKYlchsj8FERGYx43TYFpV/JIi4nz53p+228jzW6Usr2HkPvhHSkCK7XpRapJeUsSWppvdSzS47BzLnCkecklrOVU1kq1qZiqSl+by0NN/sltynU0X4QD1V8raT6XbNoRvMrMUcUOEb5v9708Ye3ce+1MTrtPiGdvEDk5sVLRdG4Xr06BEcD06H73DFMu2J62yzJZvO2XVLu2Fy434lsiXC5uwsNckborWvZKdTRSZMmBC+VcXugW0jH9uTd48Kw7aX3FG52vu/t56yMeceb8cedaxddseTpebqVBMWiNL0KFrA+v6kG6xvjyans2Bvu+rlOWuSIXsj9e3bN+w7k6X9JDudKvLiiy+G1dzsWTxXyJsP2cD1uzbVxJa1UyZWWY0941175rGH7G8vTrWOsOX5fffdF5pX7Jmcpf2kZqfD51OmTp0aApuUE4R9ekrvcTX97Ayco+z5X3rpJevdu3f41jhDzD5vzC1K8+le31JuChN7HOuLcJz2zjsv2iX79wp9TmsNGGb/fvc9e3/aO59xA/8dm/beNJv85xHW9zuL2uI9t7IRj7z2OXux3RgT15NLoNO8X79+Nnny5IrcarijcadNm9b8620Mqdnp8OlbhmFZGsAqWla5srqVFc6sbiWQTho6YfQcoxdX+hjL7uwK/pyEGOv8lBPMaE+fPn3CyIDXCyt/jLluceN7BJZeXN2jIq63W8Sl38ZzeU4xl5jAj1Bc0uFeOORiO/OQHWcOmXf6im2x19E2eOhlNmbUSLto6BC7+JJLbeSY0XbhGYfZDmsvE/qmFvr2pnbqBUPsgvNn3hPsYsvbVRnCOZr08FQGz2XlNLHKzvWU5RbZ5eOGDAjQTGbzM46LuMKxXXS6Nt0zyiYuwXPhcB5xvd0U19v13LgMRVx4KbvEI0eObP71NobU7HT4L8F+rrSL6RfQXq2KPa6mL8I+LRWK8qeOU+kpXJTGfrOs1eHLnuAirsfEBH+PwIwgiat9bWMuujJc0jyuhUtczOV724/Y+MuOtTW7NzmezovY11fvbXsNPMpOPescO+fMU+zgvfrZykvTBOtk3/zh/nblhAfsH0/+wx5PlEE4LkOqvGDt+RtzhT1XuJJdMNs7ML+IiZIMJfMcU3Z9vjJ2hYlTXO217LnwfD50wilubLcsF4ye0OGHzOdG4YdATYcZvXOPzLCX/nytHfmTjWzprgtZtyWWsp7Lf9OWX25ZW7LbQvaVnmvZgJOH2aQ3pjfzG1tYAMvkyNyf0/6SnU4JYXtLZiYXze+Yo+XjD+2t1561ByfcbFeNHmmjrhhrdz0wyf719vsdovNYQtOjbac+ZGmpZKdTUtjUm10E227oPEu9hA3o+KfBTO4s7S/Z6ZQU2snM5GWf3SwdS9iVkWfHaE6W9pc2cTrsWscsT7bbJNx///1fwMSEBx988At60nQsfYrLyJmw1wt7PThlqxJXdplAR5rPxwcH2Y/4kEMOCX08suG5wthBz8suuymutihtCy68alyw7BL4jlbMRV9klzR0OkdbcClDzC26tiKuLzs8OOLyz4IRK+bnMACS4soWx9KrDJ6bKgM45oLhSi9cya4wOpVBWOdAr/J6u3EZUlx0wgQ6l9trmUSbOB1WsjLCwxAdQ3YMT4K1kTSYmGOGHdlUmjQCmDTlA4srvecSyy7DgcTkTdlFH3OLylDEBaNnGHKXXXYJnxdmw2uVN8WVXW2SHXOFi7gqj+dqmkI1LulluSpDrVydg5h8ZbjwauFyrHNU4hKLG9slZkMz9ixi/Rz9OipDNbtxeeN3Q1z0nkuauDoHx0Vc7KS44CK7KkPKrvKJqzTOI1tc3/XXX28zZrTPLmy5eVWDsPcwq5SvvPLK5pQsjS7sG7Tzzju32w8syxclO50ahYlWG2+8cYUNsLI0ijz33HO2zjrrhH2FsjSOZKdTo/B1zS222CLMNs3S2MIugTSJG3WLh7lVstNpgbAjG19ceP311m4ommV2CZMB11133dDpn6WxpEVOh3kP9IbTC04vuXraidVTDkYnvXrT1buuXvRUPtn2uIjr7Xq9P2+qDN6u9HE+rxcm3z333BOGYPncC2n+elL5imy1JhTZTGFij2O9cKXrLuJ6HOtjLset4VZ7vujFYd+cbbbZxh566KFCrs5Rxm6KK1zE5b1oD67eR8+F1yjfcG+R02GvZNaw0MRga09GdtgukZg0tklkMRz7tggTey48z0UHX/k4Vj7PJb/nervSey48grC44CK7niu9uKSznSUdlOw1zIRBJp2Jq3wKPi2lLxvI63GRTbC4YH8PxCUWLrpucHzdlbj+mepdEDd+puIqH2noOF8lLu9ciqtzoGdbUmYes1kZIzbatpORq5ibKoNwEResaxMX++LG5U1xVfYiLjjmkoauJVzSKN+zzz7b/AtuX2mR06GNzBYXc3PgCw48SDoq2f6C2l+Kl0P9Al+8ePjhh2311VcPTWCeUYo3t4ZGGcHLfTqtEB4iHZV8BTRL+8v06dNthx12sEMPPbQ5JUsjSnY6rRSGZemwZD+TLO0rOJvNNtss7IWcpXElO502EDqWV155ZbvhhhuaU7LUW+i3WGuttcKSnCyNLdnptJGw7cVqq60WRkuy1FdYhkM/Tv7KQ8eQmpwO3w1ichx7rhL4ZlJZXJaL/dnNTeXTdcVcpRVhuCyPoH/nxBNPDItC6cykU5P0mEssG7GtGBdxY7uKW8uNsS9vmXsibpFeGFs+vYw+5hJzj/kaJw6HURqOxW1peSvlS6XNLm6Z9FRIcRttCUhNToep/6eddlr4cfERehZ5ss/McccdF74PzWdVTjjhhIDRozvllFOSXHgxFw6YPBwLp+yKm7ILH0xaigsu4sbl9VyVIeYSK50P2PFNKT5FzGI87HO/vF1CXF7ua8qu52LHlzdlV+VNccGpMnguMWVKlZe0lnC5NmKOxeU6PVf3IbaLPrYLxiaLOPmAIE6HBY7Yj+1yjD2dQ3ZJ83aJYy72SCcNnfSk6dq83SKux0V2lV9YsbhK8/oU16fpuhptgmRNTof/JAwPv/DCC/b888+Hz7OACTFG73FLuKl8Ka44Mdfjanbbgsu9+fe//x1epu7du9u1115rU6ZMSXKVVoTFVXoZLse1lDel97hWro5Teo9lV+mVuDHmHrNPN3NccDj05bCNLN/rrqW8wqm0tshXS6hmtzUBO9R2Gklyn85sErYQWHvttcMeLlnaVmhScW+ZCJil40l2OrNRmBG7yiqr2NVXX92ckqW1wtSEVVdd1UaNGtWckqWjSXY6s1kYWeG7WWyclPdXbrnQRDjssMPCt6vyCGHHlpqcDtPKeeBse8gCMrZuBLOojHRiAuno0QmLC24pF9yRuGxxSicea2AWX3xx23HHHUMac0mU39slJl3nQK9zkIYu5voyeO7ssluWS9xaLk1Tvh0FxtnQT8YGanzLibRa7II9V2kex1yP43yeC/b6WrmxLaXHtjxXuFKQzUbbDaEmp8MnShldoHecbSDVUw6mF59RCfWYk6ae96OPPnpWD7y48DwXnTAxeWMu2HOxSxkqcVUG2U2VIbYLrma3UnnpSBaXmMWh8FmIyAfq1lxzzcCn9uO53D94Ogd2KUfKrri+vNW4sluNy3HRffBc4pgru6ShU77YLjZjLhzZHTRoUNAvtdRStsQSS9huu+0W9sfhnnEtRWXArspLmrhgz+Vc4oKLuJRBXDDp4JhL8FzZFVdYdqVHp3RidB6LSxpcAmmKpVeasPJQpg49epWldcI8p8svvzzsPHjEEUeEOSFZ0vLqq6/aPvvsE7aouPHGG5tTs8wJkp1OO8jTTz9tu+66a+jrueKKK8IK4CwzBUfMtgzUBpmHk7/IOedJdjrtKNddd13Y+nT33Xef66fw08nOdhQ0QbfddlubOHFisybLnCYVnQ4dxzfffHNYV0QH3tixY8PwL8dgYo6vueaaoCf2OMUFx9wiu+3FZVLf7LDruSwOJbCJE0PAiy66aOi3YON30rnv2CiyK53OgV2doxYuNS10lbi+DNW4vgzicg7SlI/7y/G4cePCnBvuAd+m4lMxmn9Dkwp+bNeXJ7YLRgeHNM9VeVNc6WvlSi+u9OikVxmEiWUrxjEXHHMrBe7HnXfe2fBfvqjodNiYips4YsSI8CKMHj064OHDhwfMjnkcM2cCPT8YApi0FBccc2UXTltz6UNJccGeS3nFHTNmTCg3x54LR7ZibmzXc315Yy4vLQ6G9D333DM4H0ZpaFqwQyEvHM8AfVF5ZZcARo8OTiWuyliNS3mLuLo2cMou5QUTY4/7xfWwVmqPPfYIncSEfffdN6TjkLgnylfGLsfSU54UlzRxlc9ziVNcYXGlRye9x+ISqnGJxS3CcZqPYx7P5Pbbbw99h40suXnVQMKOjAwRMyKy0UYbhSF2Por21ltvNTM6vrAshB8I+xfzDTEmUDJdP8vcI9npNKiwhovZt3369LEtt9wyTFW47777wu54HU1YKEy1n2Fs5tvgcPhPzxSMLHOflHY6tBNpbtHhR0hhYgILQ2M9aTEmpLge15ubytcWXOkrYcVUj/WtJn6YVNP58sQmm2xi/fr1C/NT6HiOF/KRh+ekMsR2W1PeOCgfsS+vhHJT1cfR4DSp1bDynr4ajdaRx58/FSqVIQ61cOf0wL1o1L6d0k5nwoQJNnDgQDvqqKPCi3TIIYeEmAlbbBPJRKTDDz88BCY9kSYumDSOhZmnQkhxiT0Xm3A5RzUuPPhwmTZfxEUvri+DcJHdWrmUgXsER/csxfXl9XaZ6MU2DtR0+vfvbyussIItvfTSIebbW1tvvXUY7aET+qCDDgr5cEoEJoaRDzsEnYNJlZwHzLkoX1xeYbgEyuknpGnyHhhbAwYMCH001GIYkaNsK664YvhiBnsMsZc0ZWJyH/bJg13OQdlUBjDn4hg9aXAJ0qODk+LKNumkcSy9sPQ6VloKVwuVuLFNnVNY+lRZpSdwXdKT7q8bzD2EB0fPjPeAfrNGW2GOlHY6zJ9gWwG2EGDi1ssvvxxijj32+vbmetyWdmvhetwaLts38N0imirEbOPAEDMvH/0/PXv2DPvK4Jh48Xjh0LMc4Mknnwz56RviJeQTQmz2hC0CtZKpU6eGWAGeuMSckzkzfMSOZh4jT8ynOfjgg2377be3lVZayZZffvnQHGQ2LM0pyk4+3p033ngj5Nc1+lB0H1KhiFstX0cPtVw3abwzLH9oxNpO7tOZQ4Q9Zmi6UJugKda3b1/baqutQmc0NRC+WEFNh43FGOVglAjHQDNNH20jgEkbP358GKZlBI3OXv6jMsJEjQrHRpOJGhY1HGovfC88b4iepYxkpzOHCv0mzHymWUynLfv7UAXHSdDU2WmnncLnWpgfQ6CviBqLjnEsO++8c+Dut99+obnF7nwML+OUqGnRd5AlS62Snc5cKjSbqJkwhE3Tiyo5zR8waTTFOuJIWZbGlxY5HUYdaKf7QLvfY/oKdOyx9B7H3FhfhKvZ9bqYWy3E+eeEwDWxUTu1IBwKM84Z5dCojzABHRycE3noA0rZrGeo9kwqPf84xFy9HykbqbRa9B7XwvWhNVz9phqlZtoip8NLyB4x9A8MHjw4tPnZq/bcc88Nge9Gk8Y8E4JwigsmDZ245BcXHNv1XG835hKnuKSDibkGYXRej85jcYXhKhaW3qfFXKXFuhin0sC+rF6v9PhaYixb/rrBurfiFt1Pgu4ndlL3XraE4SofaSpvikvsubLr3xXSae7JLjj1Xuk6i7hwPNfbJUiv8nouGC55dA5x4fAbaQ0Xnsqj35u4lIVrSXG9XTAxeprbjSAtcjr8J2QjJTakYqMlbVZF7DGxx5W46Iq4YK/XcRG3KF8qTVjpqRDn87o4rZqtlgaVNcY+6BpjrsoU61M4xfW4rbhgr6/EJfY45noc64X5LBBxLXY9F+z1Mddj5Xv00UfbjIvec8Fl7CqNwAhlI0ju08mSJUtdJTudLFmy1FWy08mSJUtdpUVOh9ErjW7kkEMOHSM0ypYXLXI6DJ/SU06vOL3oZ5999qweefWkMxlNPezoiVNc6Yu44BSX3vlqXGLPJeaYdPXup7jSi4seLkF6j+GJS+y5wkr3eo99mg8xz6cR/PlJ92UqUz6vj+9R6rrRgT1X915cMGnVuDpHNS48Au+NuKTzjsElgD1XdlUecWUXW+iExdW7m+L6Mni7xCqDt8tvJLYLV/lI0zlSXH9t+r3FXHDM9Xa9rQ49esXK4Mcffzz0ojOKRaxjYXrN0QkTtwWXuFau9DEuy/V2fb4UN9anOP7Yp8f6GMdcj8X115K6Ln8ttVx3bFfPrIhb9EyF25LrsbhPPPHE5/IxmkNcya7HnuttFdn1+Tw3ZbeIS1x0bejRxVydoxJX+jx6lSVLlrlSstPJkiVLXSU7nSxZstRVstPJkiVLXSU7nSxZstRVstPJkiVLXSU7nSxZstRVstPJkiVLXSU7nSxZstRVstPJkiVLXSU7nSxZstRVstPJkiVLXSU7nSxZstRRzP4faXW49x5SdcsAAAAASUVORK5CYII=)
physics-General
physics-
A uniform rod of length 2l and mass m is placed on fixed sphere and the rod is held horizontal. The rod is released from rest with one fourth of length on one side of sphere. The normal reaction of sphere on the rod as soon as rod is released is
![](data:image/png;base64,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)
A uniform rod of length 2l and mass m is placed on fixed sphere and the rod is held horizontal. The rod is released from rest with one fourth of length on one side of sphere. The normal reaction of sphere on the rod as soon as rod is released is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of length 1 is pivoted at point A. It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in fig, impulse delivered by pivot is zero if x is equal to
![](data:image/png;base64,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)
A uniform rod of length 1 is pivoted at point A. It is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in fig, impulse delivered by pivot is zero if x is equal to
![](data:image/png;base64,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)
physics-General
physics-
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![open parentheses g equals 10 text end text m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
A rod AB of length 1 m is placed at the edge of a smooth table as shown in fig. It is hit horizontally at point B. If the displacement of centre of mass in 1 s is
. The angular velocity of the rod is ![open parentheses g equals 10 text end text m divided by s to the power of 2 end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A small block of mass ' m ' is rigidly attached at ' P ' to a ring of mass ' 3 m ' and radius ' r '. The system is released from rest at
and rolls without sliding. The angular acceleration of hoop just after releases is -
![](data:image/png;base64,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)
A small block of mass ' m ' is rigidly attached at ' P ' to a ring of mass ' 3 m ' and radius ' r '. The system is released from rest at
and rolls without sliding. The angular acceleration of hoop just after releases is -
![](data:image/png;base64,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)
physics-General
physics-
A smooth horizontal tube of length l rotates about a vertical axis as shown. A particle placed at the extreme end of the tube is projected towards 0 with a velocity
, while at the same time the tube rotates about the axis with constant angular speed
. The path of the particle is given by
![](data:image/png;base64,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)
A smooth horizontal tube of length l rotates about a vertical axis as shown. A particle placed at the extreme end of the tube is projected towards 0 with a velocity
, while at the same time the tube rotates about the axis with constant angular speed
. The path of the particle is given by
![](data:image/png;base64,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)
physics-General
physics-
A disc of mass m and radius R moves in the x-y plane as shown in. The angular momentum of the disc about the origin O at the instant shown is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZcAAADXCAYAAADWSRzVAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AAC7eSURBVHhe7d0HdBRVAwXg0JHee+9FmiBVmhQBRaSpNJGiqCigWBBFpSogYMcKAtKk+CtILyJVUJr03msIJEAIkOT+uS+zZBl2w4SsQJb7nfMOzMyWZLOzd1+dAIiIiPiYwkVERHxO4SIiIj6ncBEREZ9TuIiIiM8pXERExOcULiIi4nMKFxER8TmFi4iI+JzCxebChQuYMmUK1qxZY+0REZG4UrjY7Ny5EylSpEDTpk2tPSIiEld+Ey5hwcewY8N6bNjwLw6cOo9wa78nEWHncGjbBqz/ezP2njiHq9b+yMhITJ06FQEBAShXrhyOHTtmHRERkbjwk3CJxJktP6Pbg1mRInV2VOn0Gf45F2EdswvDvzP6omb+1EiWsxb6zdyGC9aRy5cv48knnzThkj59ekyYMME6IiIiceE/zWJhJzB3YGNkjAqGgNSl8OrELbhkHXIXdnQJ+tTMEhUgiZCv+WD8dTImhA4cOICsWbOacGHp2rWrdUREROLCr/pcQg/Pw2s1osMhW+23seSYLV6unsfyT1sjR9TxxNlrYcj8I3Cv34wZMwZJkya9Fi6VK1fGvn37rKMiIuKUn3Xoh+LfiT1RKl1UOCTKgbZfrkCwW3qc3/4zOhROHhUcGVC9x3gccsse9rc0btwYiRIluhYuadKkwdixY61biIiIU34WLlFCNmFU21JIHhUOKUt2xoxdIdH7L5/AL29URsqo/elKPIkxm89H77fs2rUL2bNnvxYsrtKtWzeEh8c2PEBEROz8L1wQicClI9EwP5u3UqH2e/NN7SVk7UjUYo0maR60+GjptU58l08//RQpU6a8IVwqVaqEbdu2WbcSEREn/DBcooSfwsw+9ZGFAZG7Bcau3YAxXUubsMj10KtYcOrGkWT16tW7IVhYkiVLhh9//NG6lYiIOOGf4RIlfO90dK6UOSogkqDs481QJnUiBKQvie6Tdl/XiU8bN25Enjx5bggWV3nxxRcRFhZm3VpERG7Gb8MFURGy/tuuuD99YiskkqPUU59hu2vGpJvBgwd7bBJzlVKlSmHz5s3WrUVE5Gb8OFyihK3AG7WsGkmuhzFyzTnrQAxOnPTWJOZefvrpJ+seIiJyM34dLpH7J6N96QxR4XAfar09B0HWfncrV65EgQIFbggTe3n++efNopYiInJzfhQuEbgcGoygM+dw/sI5HNm6HKPal8d9UcGQ7sGXMe+Ih/awKP369UPy5Jz7Eh0iuXLlMiVfvnxInTr1tf3c3rp1q3UvERGJjV+Fy6G/JqDn443Q9PEmqFGSnfkByFC2FT5f7nkBysDAQDz00EPmdtmyZcOrr75qFq58+OGH0bNnT0ycOBENGza8FjAcrnzlyhXr3iIi4o1fNYsFbZuL95+ui2pVqqJWw5Z4sd/nmL3xBCKt43ZHjhxBs2bN0LZtW8yfP9/sCwkJMYHTv39/s83bfP3118iSJQvat2+PS5c8rVgmIiLu/KvPJTIcoedO4Mjhwzh68ixuVse4evWquX5LUFBMb8zRo0dNuLz77rvWnmjsm9m0aZNZJkZERGLn1x36t8JbuIiIiHMKFxuFi4hI/ClcbBQuIiLxp3CxUbiIiMSfwsVG4SIiEn8KFxuFi4hI/ClcbBQuIiLxp3CxUbiIiMSfwsVG4SIiEn8KFxuFi4hI/ClcbBQuIiLxp3CxUbiIiMSfwsVG4SIiEn8KFxuFi4hI/ClcbBQuIiLxp3CxUbiIiMSfwsVG4SIiEn8KFxuFi4hI/ClcbBQuIs4EBgbiwIED2L17N3bt2oV9+/aZ8+fKlZtdYFzuBQoXG4WLyPUuX76MVatW4euvv8bbb7+Ntm3bonbt2qhQoQLuv/9+lCxZ0pTSpUujbNmyqFatGh5//HG8/PLL+Pjjj/HLL7/g+PHj1qPJvULhYqNwEQHOnTuH33//Hb169UKNGjVQsGBBFCpUyATHE088gRdffBHDhg3DN998g7Fjx5ry/fff47PPPkOfPn3Qpk0b1KtXz4RPnjx5UKpUKbRu3drcfs+ePQgPD7eeSfyVwsVG4SL3qoiICNPM1b9/fxMKDJPKlSvjhRdewK+//oq9e/eaGgiDh7UZbxgcFy5cwOnTp3Hw4EGsW7fOBFGjRo1MSLEwaP744w+EhoZa9xJ/o3CxUbjIvYi1iX79+qFIkSImVFhjWb9+PSZNmmT2nzlzxrrlrbt48aIJqC+//NKcY7ly5TK1oIULFypk/JDCxUbhIvcSfqizOYuhUqxYMbz11lsmAGj27NnImzcvOnfubGorvsSgmThxImrVqoXMmTOjS5cu2L9/v3VU/IHCxUbhIvcKNoF17doVGTNmxHPPPWdqLy5bt241fSVPPvkkTp48ae31PTavfffddyhevLgZDDBv3jzriCR0ChcbhYvcC/7++288+OCDpv9j3Lhx1t4YH3zwganJHDlyxNrz39q4cSMee+wxU4v59NNP1eHvBxQuNgoX8Xf8IGeHfcWKFU3I2J04cQLlypXD888/b+25Pc6fP4833ngDadOmxSeffGLtlYRK4WKjcBF/tnPnTlSqVMnMUeHkR08++ugj09n+zz//WHtuH45Ye/PNN03A/PDDD9ZeSYgULjYKF/FX7JSvX7++mfC4bds2a+/1OHSYzWGvvvqqtef2u3TpEl566SXTFzR37lxrryQ0ChcbhYv4q6FDhyJLliz4888/rT03+uKLL0xHPpdzuRl2xsc23yU+OE/mkUceQdWqVW9bv8/dhvODqlevjiZNmpjPo/Hjx2P16tU+GRZ+OyhcbBQu4o/YHFa4cGH07t3b2uMZP9CbN2/usUOdo8s4A/+pp54y/TVc7oV9N5xo2b59ezPqi/01vsJJljly5MDw4cOtPfeWzZs3I3ny5AgICECSJEmQIUMG5M6d29QsuVJCx44dTRMml9dhTZR9VlzXjU2LdwOFi82xY8dMuLz33nvWHpGEr1u3biYMYlvja8OGDWb0GCdOuuMH1ujRo81cGH7YFy1aFA888IBZFobfrNl/w+DKnj27CZtp06ZZ94y/vn37muf11j/k7zg8nMPBkyVLZkLGXlKmTGn6p7JmzYr8+fObJXd69OhhJqouXrzYzB1iTYc1wdu9oOgdDRcmbFhYmClsZ3V9W+KL4Nrvfvzq1avmOP/ltv2468XjshOs1jPJWW13HXdV4d2f135/V82F6yO57uteIiMjzWO47uN+jNuubw28r6fjrt/R23HX78ifxdNx1+/o6TVgcf2OfJ7Yjnt6DVzH+Tt6O87C4yyefgcW3je24/zZeNzT7+g6Tt6Ou78P7Md4+5sdd72GfJ64Hmexv0buP6Pr/+6vkeuYe3F/n9iP8TFcr8HNjnt6jbjt/hqwH4XzSDi82HV799+R23weNpsxJHjuuI7Tzz//jDRp0pgPsMaNG+Ppp582i1e2a9fO1FhYWJthf0769OmRLVs204TDGf4cjeZeNm3ahC1btlwrvA2bf+y3Y+GoNq5ZxuHJQ4YMMeHn6Xb+Wjiggq/RjBkzUL58eY/h4qkkSpQISZMmRYoUKczfrUSJEqY2ygmyY8aMwbJly3xaw/TmjoYLv43wDc9aAr+h/PTTTyYQ+M2JzVLvv//+tcLjnEnMTknOHObqrPbjTGum9Ouvv45UqVLhlVdeMW9KHn/nnXfMCq2HDh0yb1Juu9+fS1zwOJeiYJWzZs2aGDx48LXj/BlZ+AdnAPFxeR/3x+DPwPZsLkXOoZT25+Afd86cOQgODjZNCPbfgYHGEzkkJASTJ0822+7HeXu+Brz/rFmzbjjO14xzBPgaLFmy5Ibn58/PajRrZ2vXrr22z/04/x6coc03NX9/99+Rx/kc/IBgEwmbK9yfg8e5vWLFCjPxjk0o9uO8P1+DoKAgs4ih/Tifj68Bf8cff/zxht+Bx3mC8H3A2/E+9uNfffWVeXwuvMh97rfh848aNcqcXDzJXO8/9+P8vfiBzL8119lyP87H//DDD00zBD+EBwwYcN1rxP9zHz8w2VfA94n7/V3/Z5MP3yd8LvfjLPyd+R7n+4C/C38m9+N8n/F357kyYcIEs+1+nO8Tfijz/nwcfvDfd999ePbZZzFw4EBzez4u3ydLly417yPuZ02E/S1sOuNrxPc58efhh1a6dOlMnw2bZ/htmYWPyw8ydr7zGD/MeNvUqVOb2f0cdcbHZG2HH3IMCn74uT4IeT/X7eyFTUD8Ns5v5/ygzJkzp3ksT7f118Lfl81grDG6XjNfFJ6b/7U7Gi6cBdyzZ09TuDw3Pxh5wvFDp3v37mY/1zhi4Ta/WfGDcerUqWY0if04PwxZFWS7MV9AdoQxaHicQcOThB+aXD7cfn9WJXlSTp8+HVWqVDETzDhixnXc9XPyQ5tVVZ6QvI/rOAsf87fffjMBxpOVv5P7cS4AyODk78CTl7e3H//222/NBx9DhE0Z7sd5ewYg7z9lyhRze/fjfD5+WPL5GT7215A/L+cR8Ofnhwr3uR/n//k6/fvvv+bDkUNCue1+nM+5cuVK7Nixw3zouf+OPM6fmeHheg34M7gf5+/AZT9OnTpl/p7243w81wcfTwD352fhNhdB5PuEQ1X5O/F+ruPcZiDwNeQHMI+5H3e9DxgeHInk6Ti/BDA8+D7hMfe/M4/zPfXXX3+Z14n73O/P2/J9s2jRItMkwdu6H3c9n2sZer6G7o/PwudgaPA14pcB+/uIryGXv+dxNlfZ30fcHjly5LX3Sb58+cwHOPfzZ+O/PFf4GjCA+Tfl/rp165rAYI2EPxf/xsRzwhUsXK6ladOmJrA6dOhgavkMjGbNmplwYs2FzWP82/FcYYDzywbf11wNgM1mrnDh7VnD4TnLv4Wnwsdg3wJDhoG5YMECj7fz18LXj1+y2K/lHg5OCoOboc7PM9Y4+Tdr1aqVOa9dS/z8l/yuz4XLR2TKlMm8uPzwiiuesDxh+O1TxB/wS1anTp2sLe8Ylly0cubMmdaeaGw6Y5hxeRbWTPhBz7kyrN2zNsJWAgYYg4kfgmzGcWGA8YsSP9zcayy8L7+AOMEA5Dd4dnDfa/gFhCtIu143T4Wd/uwrY4gw5LmUD79g8UscvyDxS8ad4FfhwjZuNjG4XnSOaDl8+LB11BmNFhN/wr4dvp9Zg3L103jD84dNwqz98P92/HBnMx+b1+rUqWNq9wwa9sWw9sOmYNewYQbVoEGDTIe/+wchC+fZ8LhT/IDk87CGcy9hMNtrLHyt+bnGi7GxBsovwWwm5mvDEYHsP7tb+FW48JvQww8/fO0PweF77EOJC4WL+BOGC5uf2NR3s3Ah1ijYtHkzPE/YvMrmXTaVuTCAGGQcQeb+oegq7Edgs2lccG5HgQIFTJPYvYRNsxz99cwzz5h+PjYLsmWGrzFbWO52fhUufNOyiu7+ZmbfCEfQOKVwEX/DwOC3XPcRYN4wWNjUxf5QJ9hkxcdnHxSbYzgqzf38cy9sUruVNcPY78LO/eXLl1t77g0c6ce+Qw5uSYj8Jlx44nCkjv0NzTd7XNocFS7ib9hBz0EuZ8+etfZ4x9oIax0MDP4/NqwJseOenfisWdjPPXvhpZFv5aJgHODBviBvS9bI3clvwoVDY9lebH9DsxMxLteIULiIv+GSLvzwd7KkC3GOBWsvXBmZnfv2dnwOceYIsgYNGpgRZPZzzlPhbTkC8FYwHBs2bHjL95c7w2/CZf78+UicOLHHNzaHu7omld2MwkX8DTvPGS6ertvizfbt29GiRQvTHMWRXuw05jB+duiz38S1LImTUqpUKcfNbHZsFipTpowZYu9pkIHcvfwiXDi7mHNUPL2xWThMz2kHmMJF/BFnzz/66KNxapZiXyXn4zRq1MjMl+BwY06O5DnFL3JsDmNhPyePuyZQuhfOgYlrB747zmXiCClOOpWExS/ChcON+e3G/sZ2Fc7u5eRGJxQu4o/YvMUPafu6YU5wxBkn3XG2PzvkOQGTE1m5igQnpHJYMpusOKnS/bxLniIlvvj81meCs9bCNczatGmTYDu172V+ES5sEnN/U9sLv2VxbL4TChfxRwwIrgnGfhSuvecrnDDJ4f/Epqtr51ySpOj5QicEBoXg6tVLOH/BWbO0O56DXPKFSxVJwpPgw4WjxLichnuYeCpOm8YULuKvuCYcm7Y43PhWRm15wqWYateubf7PgQOu86103uwYO24a9p6LOnD1FNbP/xlTZ/2D0w5Xg2dLAwcLcKa5a5FPSVgSfLhwgUQOU3QPEha2Bbtvsz2Y6yzdjMJF/Bk75nlusI/S6SCX2LBpjJM06fPPPzfnWvbEAXjy2dcx+c/1WDjhG/y+NQi7F4xE63ot8O3mm19cjP0rXAuNK/ny/JaEKcGHC4dEugKEq7VyyYmWLVuapSlYTXcfnswOzZtRuIi/Y78Jv2zx/IhvrYCd9Vz7iiZPmYqC2VMjb76q+HjhUVwJnIOuVepg0JqzCNw2GR0fqoq358ReY+JESX5Z5ACE2K49I3e/BB0uHH/PdYoYHJwdzBVEiavxMiD4rYcTwdgBydtw8TsuUx4bhYv4Ow7p5WrLDBguLcLVm28VO9pdK+wGnT2AT7pUxwNPDMFaNof9+T5avjwWe0IvYuf011Cr6jOYcsjzcGL+TFwckzUWrs58r17a2J8k6HDhDGFOkOTS1JzY5cIqv/u1t/nG5eJ3XPr7ZktgKFzkXsBzh9dP4lUeuQw+R4LdCs5fYV9LtH0Y2+1xPPnGVByKiMTmLz7A52uP4GLQVozu1hCtBy/FBeuW7jjak8vqs4+Fy9SoxuIfEnyzmCeucHG6pLc7hYvcSzjBkivs8mJUXbp0MRfSc7IGmQuvmcOlYqKdx+KPX0O3Vwdh4pzFmDPuc3w+6X8Y/9kA9P1oKnZetG5m4QAbLh/DaQRsCuO1Xe6mVX0lfhQuNgoXudfw+uqsffB6LZyR37lzZ7MSMa/meTMcJBMTLlE1oounsGfrNuw9dgZhV0Jxcv9O7DlyBq71mC9evGiWamK/D5+PzWB8Pq0b5n8ULjYKF7lX8eqeHPHF64UwZNipzv5KXrqbTVeeahX/+9//TB+JN5ER4Qg6ew47tm8zV9fk9fa5bhmv1c9+Ul4nX0ON/ZPCxUbhIvc6dtLz2iEMgvLly5uBMLxolesa/Oyr4XWSuMDl8OHDzchMXhKZ/S8MC4744rIxvGw556Bx+Rj27bBwAUte55/rlIl/U7jYKFxEYrBfhMP9eV1/LmDJkGH/CCcls1mLkzJTpkxpLrHLSx8zjIoVK2auHMnjnL3ftm1bEzScxCn3DoWLjcJFxDsuHcOQ4EXCvvvuO3ONFgYK1xobOXKk6bthPwxHZ/Iyvb6YqCkJk8LFRuEi4hz7YdQZL54oXGwULiLOcQKlk2WV5N6jcLFRuIg4N23atOuGIou4KFxsFC4iznHhSoWLeKJwsVG4iDjnvuS+iDuFi43CRcQ5hYt4o3CxUbiIOOd+PRcRdwoXG4WLiHOcic/JlSJ2ChcbhYuIc8eOHTNrj4nYKVxsFC4izvF8Wbx4sbUlEkPhYqNwEXGO645pKLJ4onCxUbiIOKd5LuKNz8Il8vxh/DVvCr4eNRRDBg3BsFFfY9LsVdgfdNm6hc2Vc9g+/3sM6D8AgwYNxIAB/dG///VlwIABGMjHGvEZvh0/HYv/2YcQB+vgKVxEbg8NRRZv4h8ukWewekI/PPFgYeTKngWZs2ZH7rz5kCdnNmTNnhsF76+JrsN+wd7z1u1dLuzH9B4VkSxpMiRPkRKpUqdF2rRpkCaNe+G+tEiXLh3Sp8+ArLkK4IEmr2DsqiPXrmznicJF5PZQuIg38QuXq+fwx4j2KJ46AAEBOfDIq19gwfo9OHDwIA7s/gczhnfFA9kCkCh5RjR4ZyYOXIy07hjlwl5M7VYq6n4BSFn2SYyavR17d/xrlvN2lc1RZcPfa7Bk9k8Y1rMl7s/M5wlAmrKdMGVzINwe7ToKF5Hbg81iPF9E7OIXLgdnoVf9AkiTKi1qvfUrjoZZ+6+5hMXDn0auqEAIyNYSE7cEWvujXNiHn18qa8Ii3UM9MOugtd+b8CvYNP41VDRBlgyNhy3HaS9XR1W4iNwe7NDn5ZBF7OIVLhEhR7Fpxe+Y+tN0rDl0wdrr7ixmfdAU2RguuZ7ClG1B1v4o7uFS4xX8tt/aH4tzi4ejfq7o2kuNdxfi5BXrgI3CReT22L9/v5lIKWLnsw79aOG4cHI/tmz8G6uWzce4QV1QNX8GZC1SCc9+thjHQ62bkXu4VHsBU/4Nw+WwUFy8ePFaCY0qF0LO4fSxfdj810y826IMkjKoMj2EIYsO4IaKkkXhInJ7nDlzBhs2bLC2RGL4NlxCj2P6azWRJ2s6JGMIsCTNhfo9fsC2i9ZtXNzCJXm2EqjdrCM6dWyPdu3aRZX26NCxE7o+9zy6duqAVo2rIn9aPl4qFKrcBG+NX43TXmotpHARuT1mzpyJunXrWlsiMXwaLpGhp7H0u3546+138N67b+HFtvVRPEdGZMr/AJq9MBxL97sNGXMLlySps6BAifKoWKEcypaLKmVKoUDWlNHhxJKmKBp1eRdfjpuJFbvcmta8ULiI3B68CqXmuYgnvg0X699rQg9j9cQ3UTNf0qiQSIr7n/sR+89bg4jdwiVNxQ74atFeHNi3B7v3RJVd27Fh5XxMHNYddfKnQED6YmjY5UMs2GWv/nimcBG5PTQUWbzxSbiEX70KLwO3ogRics9aSM8aSPbWmLYvOHq3e5/LQz0x22MOhGH33BFoXjK5uV3mks0xcv4ueJmWeY3CReT2ULiIN/EKlwPzPsGz9auiSrVO+HHzGWuvXSB+7l0P6Rguedpg+v6Q6N3u4VK9O2buit59o3AcWjgSzYtHB0zqgk0xavE+TaIUuQuoWUy8iVe4hK77Ck0LRPeLFG37BTYFXrmuaSwy/DL2zR+KJgWSRN0mCcp3n4QDF6w6juNwoavY9b8BaJA3+rlSl26PsX+dsI7dSOEicnuo5iLexK9ZLDIMmye9hToF70OSxClQoHob9B01FtN//RXTJnyBdzo1QonMyZAsZRqUe3Iglhy6ZN0xyvk9mNSlqAmLJBW64ucd1n6vQvH32F6onCE6YFKV64Sf1h3HZQ/tcQoXkdtj27Zt+P77760tkRg+6HMJx7G/Z2Bg18YoX6wg8ufPh7x58yJfvvwoWKgIKtRpjXfHLsXB87bu/tDDmDfgCZQqVQqV2w7EwgPW/lidwaLPXkLtksVRrERpNOk9Ebsv3LgIjMJF5PYICQnB3r17rS2RGD7p0He5HHwUW9Ytx+KFC7Fk+TrsOBKEWKajxFMkIiIiPK4vpnARuT1mzZqFJk2aWFsiMXwaLncLhYvI7cEOfZ4vInYKFxuFi4hz6tAXbxQuNgoXEecULuKNwsVG4SLiHMOlVq1a1pZIDIWLjcJFxDleLKx69erWlkgMhYuNwkXEufXr12Po0KHWlkgMhYuNwkXEOV53ieeMiJ3CxUbhIuLc/Pnz0aZNG2tLJIbCxUbhIuKc+lzEG4WLjcJFxDkNRRZvFC42ChcR5xQu4o3CxUbhIuKcwkW8UbjYKFxEnJs4cSKqVKlibYnEULjYKFxEnFu1ahX69u1rbYnEULjYKFxEnLt06RKOHz9ubYnEULjYKFxEnPvzzz/Ro0cPa0skhsLFRuEi4tykSZPU5yIeKVxsFC4izmm0mHijcLFRuIg4p3ARbxQuNgoXEecULuKNwsVG4SLiHOe5VK5c2doSiaFwsVG4iDj3xx9/4OWXX7a2RGIoXGwULiLOhYaG4vDhw9aWSAyFi43CRcS5devWYdCgQdaWSAyFi43CRcQ59rlUqlTJ2hKJoXCxUbiIOKfRYuKNwsVG4SLinMJFvFG42ChcRJxTuIg3ChcbhYuIc7qei3ijcLFRuIg4N2/ePHTs2NHaEomhcLFRuIg4d/78eezevdvaEomhcLFRuIg4t3XrVnzzzTfWlkiMBB0uV65cQf/+/fHOO+/g7Nmz1t6YcHGfOczrTnzxxRe4evWqtcczhYuIc+xzqVixorUlEiNBh8vly5dNZ2JAQADq1auH8ePHm/0ffPABqlevjlOnTmHDhg149tlnkTFjRhQqVMjcJzYKFxHnNFpMvEnQ4RIZGYlZs2YhceLEJmAyZMiAZ555Bg8//LCZNdy+fXsUK1bMHGPp0KGDuU9sFC4izilcxJsE3+cSFBSE0qVLXwsQlmTJkiFlypTX7UubNi1+/fVX617eKVxEnFO4iDcJPlzYh8I+Fvcg8VRYgzl37px1L+8ULiLOsS+zWrVq1pZIjAQfLvTnn38iSZIkHkOFhc1m3bt3t24dO4WLiHO//fYbmjdvbm2JxPCLcDl+/Li5Gp6nYGFJkSIFFi5caN06dgoXEec4SnPjxo3WlkgMvwgXDkkeOHCgx2BhKVmy5HVDlWOjcBFxbt++fZgxY4a1JRLDL8KFeLnVVKlSeQyXPn36IDw83Lpl7BQuIs6xz0XX0BdP/CZcGAocgmwPlkSJEpk+GacULiLOabSYeOM34cKaydChQ28IlwceeMBMpnRK4SLinMJFvPGbcKHFixcjU6ZM14UL+2KcNomRwkXEOYWLeONX4cJRY02aNLkWLByeHJcmMVK4iDg3ZcoUc74kdBERERg+fDgee+wxTJgwAevXr0dISIh11McuHcHi0W+gXeuWaPFUNwydsgaehhuF7J6Pod3bo1XzlujS92ssPxhmHUkY/CpcuLTLhx9+eC1c+I2KgRMXChcR56ZPn44GDRpYWwkXPztee+0187mROnVq5M6dG0WKFDGfBc899xxGjhyJ2bNnm8sL8DIDYWFhcWoRuU7EJZxYPxU9aueI/hKcoSJ6fL8SQdZhOr1+Ip6vnhNJoo4nK1Af783YjKBLEdbRhMGvwoVWrFiBPHnymD8a3xBxFRgYiFq1apnFL0UkdmfOnMHy5cutrYSNUxree+89JE+e/NoXVBYOCuJyUmnSpEHmzJlRsGBBNGrUCL1798a3336LZcuW4eDBgzh9+rQJnputvO5yYfc8fNCyhAmQgNTl0P27FTgbFopjK77Ck2XSmefO/GB7jF5+FLEvt3t3uu3hwvkmXAqf11rhv74umzZtQt26dc0fZsyYMaYm4ul23sq6devw4IMPokePHh6Pq6ioxJTNmzfj999/93gsoRW2cuzfvx+dO3c26xO6B4ynwpU/2PTOMOLahWXLlkWbNm1MQHGI9po1a8zrw8dkcHkScWwFPunyINImiXrMTJXR9bXn0aBUxqjHT4EijV7DjG3nrVsmPLc9XEaMGIGaNWuiRo0a5l9fFw5HzpUrl/njV6hQwQSNp9t5KnXq1DFL+KdLlw758uWL031VVO61wmbn4sWLmw9WnjuebpPQCs/5xo0bX2v98EUpU6YM9uzZY30CehCyHeN61kGmZK77JEXxlkOxNtA6nkDd9nD55Zdf0LdvXzOxkf/+F4ULWfICYiyejnsrvP0rr7xi3lgMv7jeX0XlXivNmjUz54u/nCuDBg3CU089Zb5g2kPCSWHzWd68ec0UiIYNG6JVq1Z4/fXXTQuKV1dPY8mwNiiRxvU4qVCl29dYf/oW+3TuEn7X5xJfwcHB5hsZhzCLSOy4cCVbC/wFm+vZn2IPDU8lZ86cJkQ4QrVLly5mEND333+PRYsWmY5/R30vF/bjl/4tUDR11GOmLIxH27fBQwXui3r8lCjTehAW7wu1bpjwKFxsNFpMxDl/mufCaQu8yKA9RFgb4fqEHBXHEOnXrx+++uor09fEPl4OArolZ7djQu8GyMv+lhRF0GLg7zgaegG7Zw9Gw7xJo547CQo3fguzttz8UiF3I4WLjcJFxDmGC0dX+gPXUGT21fLS6O+//74ZDcba2dq1a02t5maXSXfqyvF1+KxzVWRhgN1XHE9/OA9Hr01juYzdsz5E44IMmKgaUrVumLDmhHUs4VC42ChcRJybPHmy6Z/0Bzt37jS1ke3bt5vm8f/K+V3z8e7jxZGCwZK6NNqPWISTN2TWFeydMwxNC0cHTJoSLTFqzk4kpGmUfhEul4P24s/p32DQGy+iQ+tmaFT/YdSpUxf1Gz6KVm0749X3P8HkhRtx8lLs188nhYuIcwcOHMCsWbOsLXHiSvARbFr1B/5cuQZ/bdqDIM+jlKNcwcmd67Fm9UosW7Ya2w6fQ0Lq4k/Q4XIlcDOmDnkOtYrnQMZ06ZA2TVpkypEPxctWQuXKVVCxbHHky54R6aOOpc+YBQUrNsXb3y/A/ove/0QKFxHnOImSTUYidgk0XCIQtGESXqpXCMmjqoyJU+dBzTZvY+zcdThw6gzOBoeYdYFCzp3FmeN7sHz6p3ipaVlkTBpVDU2cHhWf7o+FBy9Zj3U9hYuIczNnzjTzQkTsEmS4XNr7P7xULXqiZLKCj+KjOTsRerMWrysnsGz0c7jfjCVPhjKtP8LqwBvrowoXEef8qc9FfCvhhUtkIGb0fhiZ2BmWrChemLoTN+9JsYSfxtzBTZCB901UAM9+uRwXbHdWuIg4pyX3xZuEFy5HZ6BrlehrtqSq1Burz8atiytk61R0KJzE3D/PE4Ox8rR1wKJwEXFO4SLeJLhwCf1jGBoUSGTCoeAz43A8rhNYT6zF0MezmfsnKtMZ0zZd3/eicBFxTuEi3iS4cAmaNwh1crPfJAClXpiGU3Ed+H16PT5pldfcP6B4O0z+5/rx7AoXEed++ukns4q4iF2CC5erm75Dy1IpTThkazoKey9aBxy6sn8JXq8Wff/UNXtj7t7r1/9RuIg4t2PHDowfP97aEomR8PpcwrZjVNuyZghyoqwP47O/PV0g1JvL2PlLH5S9jzWf1Kjz5hQcsA0YU7iIOMeLY23bts3aEomR8MIFkTi9lP0u0VeLy9v4XSw55HnOil3gpinoWim9uV+qMm0wZl0w7BcOVbiIOMflUrhEvYhdAgyXKJGXsH5cL1TPHX21uKwPtMKQqWtw9Nx5hIZdwdXwCERGRiAi/CouX7qIkMC9WPjtm2hQOLW5fcoij+CDX3bgsocxzP9FuHCxu6CgIJw7dw4REQnrOtjiP3ideNY0OKv+0qVLZju+eMXFqlWrWlsiMRJmuBhXsHfx1+jWoCQypbkPKZKnRrbClfBou27o/U5/DBw4AP369EKnVg1RLl9GpEyeAqnSZUPZx3ph/KojXtfoiU+48PoNXBngxIkT2Ldvn1nC+4cffjCXTObVMTmT+ZaX5xaJp/DwcHMhvQwZMqBDhw4YNWoU5s6daxZq5PuelyAPC4vbCBmNFhNvEnC4RIsMO4m/fxuNPl2ao/aDZVGiaGEUyJ/PXA0uX/6CKFKsJMpXa4Cnu/fH+AWb4WFS/nWchgtDhLdle/OqVaswZcoU9O/fH+3atTMXEOKlX3mNbdaUWHhNbl6RzldLdovcCoZB1qxZr70vEyVKhBQpUqBIkSLmqpJ8j3733XdYsmSJuf47F6ZkrZvB5Mm0adMULuJRgg+X60RewqkD27Fh7WqsWLESq//ehN1HgqLqOM4xMHiyDBkyxGwzDI4dO4YtW7Zg2bJlmD59OoYNG4bnn38e9erVu3a9/tgKbzNmzBjzeCJ32saNGz1eFMteeKlfDjPmFyZe24SjwhYuXIj169fj4MGDCA0Nxc8//4z69etbjywSw7/CxQcOHz6MsmXL4vHHH8fo0aPRs2dPNG3aFKVLlzbf8DydhLEV1liaN2+O+fPnY86cOZg9e7aKyh0r7IBnQPBqimnSpPH4nr1ZyZ8/v/li9eKLL6JFixYoUaKE+dJ18uRJ6ywSUbjcgM0AmTNn9nhS3UrhY9WtW9cEVqlSpVRU7ni5//77UbNmTXPpXk/v2VspyZMnN32MIi4KFxtXzeWRRx7BJ598gl69euGJJ54w/Sjp00cPY45L4fW3+e3OVXPhN0cVlTtZFi9ejPfeew+ZMkWv0ReXwpp48eLFzfnxwgsvoG/fvubywBMmTMCpU6ess0hE4XIDV5/Lhx9+aO2Bqe6zz4WdnOwQ/fjjj/HSSy+Z0V/sCPV0ErqXnDlzmk5SkbvBhg0bULFiRY/vVfeSLVs2M7jlmWeewYABAzBu3DjzBemff/4xX8LYH7lmzRr06dPHemSRGAoXG6ejxS5evGhuy9BZvny56dgcPHgwOnXqZK5vYf9WyGYDHhe5k5YuXYrcuXNf995k7Zq19datW5uhymPHjjW1G4bI/v37zRBlbzjPpXLlytaWSAyFi43TcPGEEySDg4PNY+zcuRMrV640I2zefPNN09bNDlCJo8hwhEe9rp7n+0UiMuoYj/O1j634YsKgP+DQYQ7T52jHL7/8EosWLcLWrVvN6C9OrozrUHnNcxFvFC42DAbOOOY3OF/hCcv2aM7QF+fObJuHkT3b4smeI7Bga5C1N8aVoN2YOvA5dIyqLXbq2AHt2jyNNm3auJW2aNuuHdp37Iznu7+G9z4ajZl/bMKR4Ht3rhGHD7OZlzVvX2C41KpVy9oSiaFwseGcFg6z5IRIuXNCtsxEr7q5kYhNN9kaYsSCI9aRGJeOrECvitHX9kmeNgvyFi6KIoULoVAhtxK1XbBAfuTJmRVpUyRF4iRpUKJRT0xefwpXVZmJNzaLValSxdoSiaFwseHaSxyzz45KuTNCts5Aj1rZTWgkZrhkbYAR8z2Fy3L0qsB+g8Qo334E1l64itCQc6aG6CrBwWcReOIgtq3+HV++2xbls0fPVcpery+WHozrxYDEjv2NHC0mYqdwkbtKyLYZ6F4tMxJnKobaTRujdDKGS0OM9FJzebUiwyUpHuwyGjut/d4FY8GwlsjKwAoog3fm7YjT6g0i4pzCRe4awVHB8nL1jAhIVgwvjV2E1Qs/Rs3EUUGQxUG4dP0Gu6393l3Agg+bIwfDJVE59Ju3S+Ei8h9RuMhdIXjLDLxSI3PUh34BtB+5DBz8emjhAFRhEDgIl/JtP8Lyk4E4dfw4jruXY0dxaN8ubFw5H5OGv4ga+ZKaZrFCzYZg9XHfdGqLyI0ULnLHhfw7E688xJV686Ptx4twynS0R2LX3P43D5dKXHk6EdJkL4QKNWqiRrVqqGZKddSoWQt16tZBrRpVUKZgFtN/kyRHBbR6eRQW7w6KegYR+a8oXOSOCv73F/SqnQMBiQug7YhFOGPtp70LBqKqCZdH8Mni49beGNE1F44WS4SM+cqibrPmeKJpU7PQ6KON6qBcvpiFGdPf3wzvfPMbVvyzE4G66oHIf07hInfM2U3T0bMWaxSZ0OiNcdh4PATBgSdx/PgpBAUfw6rJb6EiwyFTHQyYuhHBwYE4fS4U4dbFPN2bxSq0/xhrzp7D2aAgc/2RM4EncHDnJsz6/BVUy5EM92UtjFodB2PentDoO4vIf0rhIndIMP74pA1ymZpFCmQrUBQlihdDYTNPpTCKFi2EfDkzISWPJ0mFLDnzR+0rgod6TsKh4OhHcNahfxFbfx2EBrl4uwBkfKA9vvrjxiY2EfEthYvcIRexZf43eLNzFzz3wgt4rnMndOzY0SrPonOXjmjR8AFkY7ikzIMqDVujc8dn8NpXS3DK6od3D5dKnb/EtujdHoRh2/8GoG6O6AmXaSs8g+9XawVfkf+SwkXumMjICESEh5tL6NpLRMQV7Pj9A6tDvwFGzDtkbhsREdMN7zxc6Dz+/qk3KqaLDphstV7B9C0XrGMi4msKF7lr7Zr9NkoyXJJUw0dzj1p7Y4Qe+gPdijBcAlD0qRH419rv3Wks/aITiqaMvk/6ai9hysZTuKJhYyI+p3CRu1Qkjm2Yhr6tW6N1l0GYvcl9HFm0K2d2YNxbUcdbP40+o+fBUU/K1QP4/bPX8FTrVmjRrD0GTN+E89YAARHxHYWLiIj4nMJFRER8TuEiIiI+p3ARERGfU7iIiIjPKVxERMTnFC4iIuJzChcREfE5hYuIiPicwkVERHxO4SIiIj6ncBEREZ9TuIiIiM8pXERExOcULiIi4nMKFxER8THg/1llzTt2208YAAAAAElFTkSuQmCC)
A disc of mass m and radius R moves in the x-y plane as shown in. The angular momentum of the disc about the origin O at the instant shown is
![](data:image/png;base64,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)
physics-General
physics-
Moment of inertia of a rectangular plate about an axis passing through P and perpendicular to the plate is I. Then moment of PQR about an axis perpendicular to the plane of the plate:
![](data:image/png;base64,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)
Moment of inertia of a rectangular plate about an axis passing through P and perpendicular to the plate is I. Then moment of PQR about an axis perpendicular to the plane of the plate:
![](data:image/png;base64,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)
physics-General
physics-
A square plate of edge a/2 is cut out from a uniform square plate of edge ' a ' as shown in figure. The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis passing through ' O ' (centre of the square of side (A) and perpendicular to plane of the plate is
![](data:image/png;base64,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)
A square plate of edge a/2 is cut out from a uniform square plate of edge ' a ' as shown in figure. The mass of the remaining portion is M. The moment of inertia of the shaded portion about an axis passing through ' O ' (centre of the square of side (A) and perpendicular to plane of the plate is
![](data:image/png;base64,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)
physics-General
physics-
The fig shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAPgAAACyCAYAAABvEgIBAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABFJSURBVHhe7d0HVFRn3gbw2Fs0RqOmWJJoVqOrG5NsdkX9zEbP5mjWfKt+6ho3xBKNbYOV2GJULFiIWFAUFARJPNYcJRaMigVQEEFRUUDpoIggMMDAMPN8895cszMw6oACk9fnd/I/KnNnJoe5D2+77+U5EJG0GHAiiTHgRBJjwIkkxoATSYwBJ5IYA04kMQacSGI2G3CDwaD+jYgqyuYCXlJSgqioKISGhiI/P1/9KhFVhE0F/N69ezhw4ABmzpyJSZMmwcvLC8nJyeqjRFReNhPwoqIi7N27F7169UKLFi3QvHlzvPnmm1i+fDmysrLUo4ioPGwi4GK8HRAQgIEDB+K5554zq27dusHT0xOZmZnq0URkLSsDrodep0WBRoN8TR4KCguQX1iM4hIDDHrjn9oCaPI00GgKUaTTozzTYzqdDhEREbC3t0f9+vXLBLxmzZqws7PDjz/+iJycHPVZRGQNKwOuRWF2Im5eCELIL8dwKjgcoTfu4LamGLrCDNyNCceFs+cQFBGPhKxClKjPssbVq1cxY8YMtGnTpky4H1SDBg3Qv39/7NmzB8XFxeoziehxrAx4EbRZUYg97ArXmTPwtaMHtgXFI6moBPq8VNw56oX927bC/XgsLmRorQ54YmIiVq5ciQ4dOlgMtmk1atQIgwcPxtGjR409BY36CkT0KFaPwQ3aW8g+74Kl/xqIvn2mYsGhaFw39sVLclKQtGM1ftywAe4XM3BZY10HXUycubu7o2fPnqhdu7bFUJcuMfH22Wef4eTJk8qkHBE9mvWTbAYNSjKD4P/tSIzv9w+M3ngK/pklyMm8hrOem+CzeRfOpGlwz4rmOzc3F/7+/kq3u2HDhhbD/LBq1aoVJk6ciKCgIF4MQ/QY1gdcUYg7x5fBx+ET/GOiJ5YfCENczM/w8/OH155oZBTo1OMeTlzIIlrgESNG4MUXX7QY4sdVu3btMG3aNFy5ckV5PSKyrJwBNzbkd/xxftvXGDpwKsaOn4e9+9dhg384doUWoeAx81+ixRVXqTk4OKBp06YWw2tN1ahRAx07dsSiRYsQHR2tvjoRlVbugEOfjrTznlgyxNiKd+0J++lOWH4iDqFZxof06jEPIa5KmzdvHl5//XWLwS1P1apVC507d8bq1auRlJSkvgMRmSp/wI0K04IQvPSf+KJnb/z1c3dsCLmNx12GkpCQgKVLlyotr6XAVrR69OgBNzc3pKSkcExOVEqFAg7NTeQd/gYuc6Zh6JIg/Hy1AA9rvEXo8vLy4OzsjJYtWyotr6WgVrTq1q2rXAjj5+enXMtORP9VsYAX3wVOrcU+ny1YciwDkXcf3nJmZGTA19cX77//vsWAPo2qV68ehg8fjlOnTqnvSkSC1QE36ApRmJWGu6lxiL0YgrOeG7Fntz8OpemQ+ojJ85iYGIwbNw5NmjSxGM46deqgWbNmaNu2rbIEJv5t+rh4rH379mjdujUaN26sXLpq+viD6tSpE7y9vdV3JSLB6oCXZCci6aQ39m9ZgIVLnTF9/jZ4H7yMxCJjg64eY4mYAFuwYIGyM6x0KEV4P/jgA4waNQpOTk4YPXq0cjGL6TGffPIJ1q1bh4ULF2LQoEHo0qVLmWvWRbdfdNN3796tvisRCdYHPCMasXsWYs0se3w+1RmOHkEIvJ79yHALYvwdEhICR0dHdO/eXZlBF1tCxcUqK1aswI4dO3D69Glcv35dCfJrr71mFl6xpCYm0ERP4PDhw8rOMrE8NmHCBOXS1X79+mHYsGFYv3698hpE9F/Wd9FzkpAe8gP2bt0MN7/TOBWXg/Ls7YqMjISrq6sS9O3bt5eZ9dZqtfDw8CgTcHHzh9KXpYodaKmpqThz5gz27duHwMBAZaxPROasn2QzjsGLstOQnpyMpPQc5D3+ojUzYhdYWloa4uLiLO7tFqEVrbOlgIvHLBHBF1tICwsL1a8QkSnrA17JCgoKsGXLljIBF1tJGWCiimHAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTiQxBpxIYgw4kcQYcCKJMeBEEmPAiSTGgBNJjAEnkhgDTs+MkpISpZ4lDDhJr7i4GLdv30ZwcLBSqampKCoqUh+VGwNO0jtx4gTGjh2LgQMHKiX+7ufnp4Redgw4Sc/FxcXsnBLVp08frF27FmFhYbh37556pHwYcJLe6tWrzc4pUfXq1cMbb7yBoUOHwsfHB2lpaerRcmHASXorV640O6dMq1GjRujduzccHR3x008/SddtZ8BJeqKFbteuHerWrWt2bplW48aN8fHHH2P9+vWIjIyUpttu8wGfOXMmtFqtehRR+cXExGDBggXo0KGD2blVuho2bIj27dsr3fatW7ciOTlZfYXfL5sJuAixp6dnmYDPmzdPPYKo4m7cuKHMoJueWw8r0dL37NkTc+bMwYEDB5CSkqK+yuMYAL0OuuJiFOkM4l+/0uth0JUofwK/rsUXF+uhN/x2RKWxmYBrNBq4u7vj1VdfNftmT5gwAfHx8cokCEveEmvTD8rS409S6enpCA8Px7Bhw1CrVi2z8+tR9cILL+Cjjz5SZtsvXbqkdNvFmvrDGQNbokF+Zjzio0IRevYMzoRFIyopBzm5mchLu4ar4REIu5yIhEwtCkueoYCLyY1Vq1bh5ZdfNvsmd+vWTVm3nDhxIr766iuWhDV+/HiMHj0ao0aNwpdffmnxmCepSZMmYcyYMXj33XfRoEED1KhRw+wce1TVr18fnTp1Ulp/Z2dnREdHq2fsQ+jvIy/2EI67TcaUT/+Gv//rW8zedQNXky7iRoALnKYuxOyV/jgWl4f7VXBRnc0EPDY2FvPnz8dLL71k9g2uXbu28k0Ws51ijMSSr8TnKz5n0bqK5SsRQkvHVbQenDvPP/+88l7lCbhpdenSBTt27Hj0pK8hH4UpQQjznY7pPV5C+zf+im6TdmLTD9tw2P1rTHFYgblbTuN8agHyKr8Bt42AG4xjETERIsbbpQPOYtlKibG5k5MTsrOz1TPXEuPYu0QL7Z1LiHQfjRmf/gWd+0zA4H/Pwrr1bvAOikPY3UJojd3zKsi37bTgd+7cUS5IKN1FZ7FsqZYuXWrlsq0B+vRjOL76Mwx990/4Y0/jUGFLGC4afzbo1COqgs0E/GHLZM2bN8fbb7+tjMU7d+7MkqS6du2qlJhUNZ34Et1n8Zm/9dZbynGiW1z6ueUp8Xxx7ohzqHXr1kp33fT8srZatGiBvn374siRI+oZa40kJByaDcf/aYu2Hf4X/eafwulU/bMZcPFT0cPDo0zAxSzmmjVrlCU0Nzc3liQlPmtRI0eOVMbHDz5vMRYXn/miRYuU4zZt2lTmueWpjRs3Kmvaonc4ZMgQ5fwqzxi8Zs2aSq9STAIePXoUubm56hn7OHogNxw3jizGd2P7489v/gV2/efA6Ug8rj5qIv4ps/kWXMyC3rp1CxkZGRaXQFi/zxJDMlFiI0jTpk1/+7zFJJv4zENCQpTjxBJX6eeWt8TylljmErP04r2sDbgItrjo5fvvv1f+f8q1xVR/GzcD9yFg5zb47d0OV4ehGGP8wfX3r32xIewe8tXDKpvNB3zWrFnQ6aqyU0NVydvbG82aNfvt8xaz3OIzT0xMVI94Oi5fvoz+/fubnVsPK7H+Lbr1U6dOVbaainPTaoZCFGRE4kagJ9Z864IVW84i7PYdpJ9bgY0ju+APf+iP3pO8sfvKbaTmFKOyG3MGnKpVVQQ8KysLvr6+eOedd8zOLUslVnFEqy2WwxISEsq/D8LYcqecXA+fGYMx1H4xpvolI0ZjPH9v74L/XDvYvfoKmncciuErj+LAtRzcr+SpdJsPODebyE2Mj0sHXHzmN2/eVI94cqGhocqFLmLyzvTcMi2x9i52lc2dOxcBAQHlGGuXYshG5qWfccLbFZt2HMO+KC2yio0p1sbg1umt8F42D3Pnr4Xrngs4l5gPDQPOgMusKgK+c+dOZTbd0thbrG2/8sorGDRo0NPbF27QG//79VrzMvl98Jje+FgVLIQz4FStqiLgYo+D6UTeg6pTpw7s7OywbNkynD9/HpmZmeoz5MGAU7WqioCL8bTYD256XnXs2BH29vbKHEBSUpJ6pHw4yUbVysvLq9IDfu7cOYwbN07Z692yZUu89957WLx4MSIiIqRvPGw+4N988416BMlIjHtNJ78qI+D379/HhQsXlPcSPYZDhw4pry/2QMjOpgK+efPmMgEXWwnFTjOxT1h0pVhylLiJgiixRdh0fFwZAX/gWQh0aTYTcNFVEj9dxfXCpgH/8MMPlX244l5Z4qonlhy1bt06pYYPH64sUVVFwJ9FNhNwcRubvXv3KreyNQ24uPBALHGIixQebFBg/f5LfJ6iRI/NdLOJuFTVwcFBucXSs9jiPm02E3Dh4MGDaNOmjVnAWc9WiaUrcfeeqKgo6JV7mNGTsKmA+/v7K7fHsfTBs56NErvJpkyZgmvXrjHgT4FNBVxsCJg2bZqyjNGqVStldlV00cVeXJZcJZarRDVp0sQs4GLr6PLly5WLTthFf3I2FXBxx8pLlyKxaaMbHP7zH2XboOiuiZvmseSryZMnK1s4BwwYgO7duytjc7HR4/jx4+oZQU/KpgIu6HQlyLx7F/G3biEuNhZxcXEsiUtMponfJBIYGKhszRRj75ycHPVsoCdVvQHXpiMr/iLCz51DcHAIQkJCcT7iFtKrajc8keSqKeBF0GtSkXLhEI7t8sJ2nx+U64V3bN+GrR4+2HnEGPq0IuRzCEb0RKon4DlRSD27Ga5Oq7Bg9X4cvXgDMTGxiLkWiAj/VVj53QrMWfULTt28j3LcS4OISqmGgGuRHe6Fgwv/DyPGrcB0n5tI/O2+NdlA0i5snf4FRnw6FYv2XUWEcTjGhpyoYqo44CKqKYj0dcTCAb0wYrYf1l8uQa5pgrVxCHb5AjMH9MYQp5+x9YoeVfAbXoikVMUBF3elDMcvLmMx9p0++NzpIHZmAGYb9gx5iPOegCX/7IpeE7dhyQkNdGzCiSqkigMufs93MI6sGA37P/aFvbGF3n0P5uNsQwES/KbAeWhX2I3bgkVHGHCiiqrigIvO9lWcdZsIB7teGD5vNzxvwfwe0YZ7uOoxDosGvY/+jrvgeo5ddKKKqoZJtmwkHXTCpn/3wICvNmBOgAb31UeUMXpxBI44jcGkjwdjyuYgHL7z68idiMqvGgIO6GIPI8xzEqZM+Q6TV/+CwMu3EBefgPi4MEQHecB19mxMdXDHD6HJSFafQ0TlVy0BR1E2cuNPImCLM1Z9uxjObl7Y7OML700uWLdsIZas3wXfM6lIzNNV6S9qI5JN9QRcUYDcG8G4GPATDhw5hsMnTuD4IX/47z+ME5GJiNeya070pKox4CYM4ibwD0r9GhE9MdsIOBFVCgacSGIMOJHEGHAiiTHgRBJjwIkkxoATSYwBJ5IYA04kMQacSGIMOJG0gP8HLElOhShj1DsAAAAASUVORK5CYII=)
The fig shows a uniform rod lying along the x-axis. The locus of all the points lying on the xy-plane, about which the moment of inertia of the rod is same as that about O is :
![](data:image/png;base64,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)
physics-General
physics-
A thin rod of length 4l, mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendicular to the plane of the paper.
![](data:image/png;base64,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)
A thin rod of length 4l, mass 4 m is bent at the points as shown in the fig. What is the moment of inertia of the rod about the axis passing point O& perpendicular to the plane of the paper.
![](data:image/png;base64,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)
physics-General
physics-
Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUIAAADaCAYAAADT70sGAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACHwSURBVHhe7d0LfM/V/wdwl/p3VfklhBRFiZTKJZTkFiL3y7CVu+R+v4uZud/vd5EilGuExCJ3c79sY3OZmetsmM1e/72PMzHDLt/L53v2ej4en0eds6+S7OV8zuV90oCIKJVjELqAsLAw7N69Gzdu3NA9RGRLDEIXMGvWLOTOnRunTp3SPURkSwxCF9CmTRukSZMGvr6+uoeIbIlB6ALc3d1VEM6ePVv3EJEtMQgt7uLFiyhTpowKQg8PD91LJrp9+zZiYmJ0ixyJQWhxmzZtQrZs2VQQFihQAFFRUforD3f58mX1TUWuZdWqVVi/fr1ukSMxCC1u0qRJKgTlyZkzJw4fPqy/krDFixfj22+/RWRkpO4hV9GjRw/0799ft8iRGIR2sGbNGhw6dEi3UqZ79+53g/C5557D9OnT9VcS1rBhQzz77LMIDQ3VPeQq+vXrBy8vL90iR2IQ2kGrVq0wb9483Uq+8+fPo3LlyneDUB4Z7T3Kl19+iSeeeIKvWC6IQeg8DEI7kO0uM2bM0K3k2759O1555ZX7grB06dKIjo7Wn7jflStXULhwYfU5vmK5Hgah8zAI7aBPnz4YN26cbiXfkiVL7gtBed59992H7if8+++/kSNHDvU5GUmSa2EQOg+D0A5GjBgBb2/vh47cEkN+7MCBAx8Iwqeffvqh84TDhg1DunTp1OdkZHjp0iX9FXIFDELnYRDagQRV7969cfPmTd2TdLJ/sHz58g8EoTwdO3bUn7pfs2bN7n5GttzIog25jr59+zIInYRBaAeLFi1Chw4dEB4ernuSzt/fHy+88IIKNVn8kJXg9OnTq3bt2rURERGhP3mHLKxUqFDhbhCmTZsWnp6e+qvkCuQPuKFDh+oWORKD0A7Wrl2L5s2bq6oxybVw4UIVaLly5ULXrl3RqFEjtGzZEhkyZECWLFmwdetW/ck7ZH4wa9asd4NQnsetMJO1yO+ZCRMm6BY5EoPQDrZt24YGDRoke45OToXIyvOHH36oVo4PHjyIpk2bqlGfjDYLFSqEBQsW6E/fMW3atPtCUJ6yZcsiODhYf4KsTv4fz507V7fIkRiEdnDkyBFUq1Yt2Zua5bzpnj177m7K3rFjhzpnHBISotpnzpxRc4hxJDh79er1QBBmypQJ69at058iK5P5ZJnjlZNB5HgMQjs4d+6cGo3JX21BRoUShGfPntU995N/z8MWViZOnKg/RVZ24cIF9Wq8evVq3UOOxCC0g+vXr+Ozzz5DYGCg7kmZxwXhzp077y6syPaZuEUVebp06cKKJi5AFsdkRPjPP//oHnIkBqEdSIUYOeq2f/9+3ZMyjwvCX3/9VYWehKEsqsjosFixYqqvaNGiCAoK0p8kq9qyZYsaER4/flz3kCMxCO1ANkPLFpfNmzfrnpR5VBBKlZm6deuqEJT5JR8fH3z33Xcq/GSVWbbd8HXL+uQUkQRhSrZcUfIxCO1AXkVbt26tVnht4VFBKBc6jRkzRo0KhWyj+eabb9TfywT8Tz/9hICAANUm6xo/frwq1kHOwSC0E9kYa6vNsY97Nb7XX3/9pYIw/oZrsjYpksFCGc7DILQTGQ3Kq6ktJCcIZcGGXIP8oSWLWnJbITkHg9BOJLxkwcQWK7YMQrOdPn1azetyz6fzMAjtRBYrZPU2MeH1OAxCs8nuArmp8NixY7qHHI1BaCdy8kPO+m7YsEH3JB+D0GxyQZecROL/M+dhENrJrVu3MGDAAFWbMKUYhGaTFX/ZAkXOwyC0I7m3RF55UopBaDbZOiMVhsh5GIR2JMelatSooe4SSQkGoblkr6cU8Z08ebLuIWdgENqRbGRu3Lhxis+PMgjNJXPJUrJN5gnJeRiEdiSnPqTqcEr/tGcQmuvo0aMoU6YMLl++rHvIGRiEdjZ8+HC0a9dOt5KHQWiuZcuWqREhOReD0M6WL1+uttHcW0g1qeIqXktB1sdhELoWuaxJbh8k52IQ2pmfn58Kwvh3jCTFrl270KJFi0SV3WcQupZ69erxtkELYBDamZTkkgWTOXPm6J6ku3r1qgpDmXN8HAah65Cpji+++MJmBXwp+RiEDvDDDz+oy7tTcuF7YjEIXcePP/6oyrUl5g84si8GoQOsWLFC1Zqz1R0mj8IgdB1STVzCkJyPQegAsshRvXp17N69W/ckQcxtVfr/dkxM7N9GIfKW/L3+WgIYhK7hxIkT6nzxvn37dA85E4PQQerUqZO8itXh57BzxSR0auGBhk07YsqK7Tj3iIxjELqGqVOnom3btggLC9M95EwMQgfx9vbGwIEDVTGGJIkdEcacWIBKb2bA61VG4sQNjghdncwVN2nSBJMmTdI95GwMQgfZuHEj6tevr1aAkypi4xAUzpEVjeY8vl4dg9D65HVYfi/IJf5kDQxCB5EALFeuXDLmCaPw1+CayJH9c/x47PE3nDEIrW/cuHFqX6jcQEjWwCB0oGRd0BN9BIOq50X2Mp7wi3h82X8GobVJJSIJwZkzZ+oesgIGoQP5+vqibNmyuHDhgu55vNtHfkH1vP9DGa+/kZh76RiE1iYnjGS1+NSpU7qHrIBB6ECycVb2E8qKYeLE4PDPnZD3f/nhvenxBRcEg9C65CKvsWPHqouayFoYhA62dOlSVaw1cacJQrGg4yd4uWAr+JyN0n2PxiC0LnktlorlssGerIVB6GByvtTNzS1xB+0vbEWHopnx4fc/ITiRp/MYhNYl58XlZsNr167pHrIKBqGDyevR4MGD0b59e92TkBjcjo5CwOoBePuJTPh2+jbciu1LDAahdY0aNYp3k1gUg9AJZE+hjAofWnUkJhx+PkvQ3/0TZH81H9x6TsGuMxGJikIGoTXJMUlZJFm/fr3uISthEDqBHKuSsJo/f77uiS8GUZHXEX4tDOEREYi4fgO3ojkidGVyb02lSpVYkt+iGIROMnToUHWfia031TIIref27duqJqVspJapEbIeBqGTHDt2DFWrVlUT6LbEILSe1atX4+uvv07UVQvkHAxCJ+revTt69Oih5o9shUFoLbJCLOX4Z8yYoXvIihiETiSnC6RUu9xSZysMQmuReeDatWsn6TQROR6D0MnGjBmDpk2b2mzuiEFoHefPn0fdunWxYMEC3UNWxSB0stDQUFSsWBF//PGH7kkZBqF1zJs3T40GIyISc0qcnIlBaAHyDSOl/G1RrZhBaA2yTUZCcPHixbqHrIxBaAEyoS4X+ciB/JRiEFrDL7/8glq1arHmoItgEFqEBFjlypVx4MAB3ZM8DELnk1dh2S7z+++/6x6yOgahhXTr1k1tsk7JdhoGofPJxmkPDw/eV+xCGIQWEhAQoI5hrV27VvckHYPQufz9/dWVDHKkjlwHg9Bipk+frrZcJLdUE4PQeWQLVOvWrdG3b1+bbpIn+2MQWszNmzdVEEogJgeD0HlWrVql5nn9/Px0D7kKBqEF+fj4oEyZMggKCtI9iccgdA45RyxboGbPnq17yJUwCC1IXrF69uyJDh06JPnECYPQ8eT/kZwZl/topNIMuR4GoUVJ0VY5cSKbrZOCQeh4v/32myrBf/LkSd1DroZBaGFSzViKMuzYsUP3PB6D0LEk/CQEV65cqXvIFTEILU72pMnm3MTeg8sgdJxbt26pgqt9+vTRPeSqGIQWJ99s7dq1Q5s2bRK1QZdB6DjDhg1TK/wXL17UPeSqGIQuQL7R5OIfGR0+DoPQMeT4XNmyZbFnzx7dQ66MQegi9u7dq+YL161bp3sSxiC0v8OHD6sQXLJkie4hV8cgdCE///yzmpiXY1wPwyC0r9OnT6NGjRrqbmoyB4PQhcgetX79+qFBgwa4cuWK7r0fg9B+zp49q+YE5a4ZFlQwC4PQxYSHh6uVyk6dOiV4npVBaB8SgnIJE0PQTAxCFxQcHKxez7y8vHTPfxiEtie/3nXq1FEhKGfByTwMQhd15MgRVKhQ4YHiDAxC25IzxFJpmiFoNgahC/v333/VSrIsosRhENqOhKCMBKVgLkPQbAxCFyfbaT7//HN1R4b4+++/GYQ2EDcn2LVrV84JpgIMQgOsWbNGheGiRYuwbds2NGnShEGYAlIpXEaCDMHUg0FoCLkX+csvv8T333+P5s2bIzo6Wn+FkmLXrl3quoT+/fvzBrpUhEFoEKlS8/HHH+ODDz5Q9+pS0sjIWgriTpw4UfdQasEgNIRcJL59+3ZVDipnzpxq0/Xx48f1V+lxZPU9bnqBUh8GoYuTkZ9cFvTkk0/C09NThZ+bmxu6dOmi7s+QV2Z6uLCwMLU1Rl6HN23apHsptWEQuig5bichV7x4caRJk0a90oWGhqprJJs1a6bmCGV0I/1SLoqT/g+S4gmyMty0aVNWl07lGIQuSL5pZVHkxRdfVCGYJUsWbN68WX1tw4YNavuM1DEU+/btUyugspLM29X+I+X15f5hKZ7AFXZiELoQOWcst6QVKFBABaA8adOmVa92cRLaUC2vf1JFWe5AidtvmFpdvXoVAwcOVFV8li5dqnsptWMQugh55ZUFkLgAjHuKFClyX4XkR50skQUVmQuTitep8VVQiqjKr2HDhg3VazFRHAahxcliyA8//KBWguOHYPr06R8Y1TzuiJ0EYOfOndWewx9//DFVHB07ceKEOiYn/83e3t5qhEx0LwahRUlALVu2DCVLlnwgAOOeuEWReyXmrLHcwytzZDI6ktfl0aNHq/nDuHlFU0joS/1GqSbdu3dv7Ny5U3+F6H4MQguSECtcuHCC4Rf3vP766zhw4ID+Ef9JStGFS5cuqbPJ7du3V2EhF8pv3brV5U+lBAUFYeTIkWrFXI7JyTUHPGlDj8IgtKCIiAhVCVkeGfXlzZv3vhB86qmnMGHCBP3p+yUlCOPICFEulJcVVHl9jAsPVxMSEoKZM2eiSpUqaksMR4CUWAxCi5MCAPXr10e+fPnUnKAEoSx4XLhwQX/ifskJwnvJK7LMp3311VfqvK2Pj4+lR1NyZYGcppGfq/w6yb5AmVIgSgoGoYXt3r1bFV+dOnUqhgwZgnTp0iFr1qxYv369/sSDUhqEceSUhYwMGzVqhJo1a6JXr16q5Ne1a9f0J5xHiiGsWrVK3fUsPzfZI9mjRw+1gVxG00RJxSC0KKmCInvdxo4dq9qyf1BGgzKf9yi2CsI4x44dUyMuWW2VUJS5RA8PD1WYQEp+yYgsobtTbEVOxMi/Q+50llHf+PHj1eu7LPTIIo/890oBVaKUYBBakMzPyTe7fPPL/J2QbTKlSpXCqVOnVPthbB2E95I5uP3796tN2TICk7PM8siK7MKFC9VCi3xdtqvIZ2UDeFJI6Mkrv7yeyyLOpEmT1J5HuZ8lU6ZMyJMnj9pKJKPV8+fP6x9FlHIMQouRI3HyOiwheC95HTx37pxuPZw9g/BectZZgks2KY8ZM0ZtUpYRbLVq1eDu7o7WrVursJQFGBnVyuLOwx4Z5Q0dOlQFatu2bdU8nwSsjH4ldOUPBumXM9NxfzAQ2RKD0EJ8fX3V+de41+HkcFQQPoyMBCW4ZA5vxowZ6jibhJgE48MeOTctRwBlBCgjX/l1iB94Bw8exNGjR3WLyLYYhBYhIysJQZn3SglnB6G9yGu3FJ4lsgcGoQVICMqc4KhRo1L86mdqEMqWHlk5J7IHBqGTyZxg3DE3W8x/mRqEHTt2TPBCeyJbYBA6kRyRk4WRlL4O38vUIJRV6RUrVugWkW0xCJ1EtpnIKqu8DtuSqUEoK+bBwcG6RWRbDEInkBMjEoJSGMDWTA3C4cOHY8qUKbpFZFsMQgeTyijVq1fHiBEj7LInztQglMo4nCMke2EQOpgUWv3333/VhmR7MDUIZcVYzlwT2QOD0DCmBqGcJz59+rRuEdkWg9AwpgahnDhZvXq1bhHZFoPQTmLCjmPJ+P5o36EXpq/eh6SVH0g+U4OQ+wjJnhiEdhGBdSOboWHncVj68xg0b9ASk9cHwBHlAkwNwp49e6oFJiJ7cE4Q3r6FqCSsFUTfikTUI1MkBtFRsf/MpPxD7en2FWxZPB8bg6QRionN3dB5sg9uqC/al6lBuGXLFp41JrtxbBBGXcau3yeiS4tv8W3Lbpiyci8uPaKm59WgXZg/rDuaf+OBJm36YMaqvbic4Ocv4I/Jnhg0fQOcXz9Z/JfaQWtGwq1eGyzcfYEjwhSQDehSgYbIHhwXhNFXsXm8O97KnhvlGrRCy/pl8UbWvGg8wQdX9EfuFea3Et+VzInsBcuiWeu2aFmrJHJkzg23kX/h6gO3Tvqj/5d5kOfroQjRPc4XjeN/jEKjWh4Y88dh2K+G8/1MDcLu3buz6ALZjcOC8NrRRaia62WU7vG7fkUMx9LupZA5bw0sPBb/pfEylnT5DM9nKo05vnHf0Jcxr01RvPBaNfzmF/9eigB4Vs2P/DVH4m7d4ujruHDuDC5cuyeCoiIQduPORUTREVdxJfwmEvcyHY3rYVdwLfJOK/LaVUTcm2wxkQgLu/fnFIOAdWPgXr8lZm09q/scw9QglPtTpHgrkT04KAijcOCXlsieuSQmbA3TfbHRtmcyir6aG23mxr+f9wq2LxmPYbM24co9F6j5zmyGHBk/xqQ98W9wkyAsgAK1RsXGZayLOzC4cTmUcfPEtkuxL6TXA7BgYFOUKVEcn5QohyYd+qNPCzc09lr6X3A+yq1jmN7ZHS17eaNve3eULl4MxUpWg9ciH2xZMQXNKpdEsWLFUO5bT2w8KcNVf3hXfQeZc3+Cet+4ocbXrTDDx98ho0JTg1CKvEq1aiJ7cFAQhmOTd3lkfrculhzXXbFu+K9F7dyvoNrQtQksJMSbUYvwRb+vXsf/inbEjpD410tKEL6HQg2n4PLl/Rjp8TGyvVMF49cH4nrUZfzWuzxeyfIevu0/FQt/HIfvK7+Lp9OkwYdNJyNRW3Qj96B/pTeQ5v9eRZWOI7FwyVx0/vo9vPjcy3j3C3d4TpqP+WM74P0XX0CZnksQEnMd50764diRQ9jvuxd79hzC6csRnCNMAbmjhPeUkL04KAjD8GfvkshcyAOr1ErqHVGBG+GeJxMq/LAcV3VfgmJHdDPafIaMGd/HDyuOxr6oxncCg2sWQv4vvkXX+oWQrUAtzNl7UX3l+vFFqPhaFlQd+Aduqp7YTPVbiq8zZ0CRltORqPvPIvdhYLVceL5QO+zSg9HAPwYgX7pn4DZ1G9SUZUwgJtbOhRyVB+GAEzPI1CCUKj08Ykf24qAgvIYNA0oj8/sNsfyE7ooVeWIDGryZCZU8Vz50tTc6ZBeGexRBxkwF0W3BTiT87R2IETXz4f+eSIM0adLitc864p8rd8Zfpzb0QN7MH2HAqnuWUW6cxLCK76Jw0ykPBGHogbUY3aurmpPq2rUbvGduwuWow/Cqmgv53KbjrF6oOfPnMHyc7W30W3PyTkf0acxuXACvVxoIX0ftnk4A5wiJks5BQRiJndPqIXuurzB/338zZdcOL0L517Kj0fgtCYzyZIFlNTpUeAsv5y6HkWsSGgnGOanm5LIVqo2xUwejXM6M+LTLb7Hj0Nhg8+mNPJkLod+Ke2rZXT+JoRXeSTAIT6ybgFofvYN8+fMj3zsFUKH5NJyNPoohX+dGQffZOKMXTE6tGYKPYoOw7+qAOx1RQZj5TX68UdkT+xiENic33HFDNdmLg4IQCP5nFD7O/CbaLziie4Cji77Da1mLYtj6UN3zn5v+a9D2i9fw6kffYNG+S7r3YQIwsEoBFHSbipjYuNw8vDpezpAPAzcGI/LcWtTIlRnle94JRnHt6EJUyvQ8irR48NU46vpVhJwOROCpUwgKPIXg0HDERO6P/efnwnuNZjEInSQgIACBgYG6RWRbDgvCmGuHMap+fmTOXwMTVmyFz2+jUPntzPig/nAclnAJ34ERHVqhx/TtsaFyCjNbfBD7mpsGheu2g9ewIRjQrx/69umNvoNmYse5+Enjhz5l34gNIW+oSA3fhZ5lsuG5dzyw1v8sNo6qh5yvvoM6Hb0wcZw3mld6DxnSP42SrWcmbo7w5h70KpMJuWpNxSkdhIErB+DtDNnRbbnfnY6ok5hc93W8XLoP9jhxV7epQfjnn39i48aNukVkWw4LQhHhvw79GpTGB+8XxHvvvY/SDfpiXYBeL768EZ1rVIL7kL8Qc9EXI1qUQ7FPSqLU56XwaYkSKCFP8eIoUbY1fjsef4R4FrO7NkTDXj8j7iuhmyaiXvky6PyTjEAjsHlmD1Qr8xlKVayLzv2Hwf2jHCgRG4SPvzI91i0/zOpaC40GrESoniMM2TYPjavWw7S4fYLRIVjh2QA1O8+GnxMzyNQglA3VcsE7kT04NAjviETIyaM4EnAu9u/s7/YVPyyaMgV/3ZtOl/5GrTxZ8WWfFQ45/+tIpgahVKgeNGiQbhHZlhOC0LFuX/ZF15IZ8UKB2hj70+9YuXQeetf/CJlylcOkf+NvzHZ9pgbh2rVrsXnzZt0isi3jg1COx108sBw93SuieLHiKF68BEp91RgT1xx2WI1ARzI1CI8fP45jx47pFpFtpYIgvCPmxiWcPuGH4/4nEXI1bmu1eUwNQk9PT4wfP163iGwr1QRhamFqELZv355zhGQ3DELDmBqEEyZMwLx583SLyLYYhIYxNQiDg4Nx9qxjS5pR6sEgNIypQTh79mwsXLhQt4hsi0FoGM4REiUdg9AwpgZhv379MGbMGN0isi0GoWFMDcJDhw5xHyHZDYPQMKYGoVznuX37dt0isi0GoWFMDcLOnTvDy8tLt4hsi0FoGFODsEuXLvD29tYtIttiEBrG1CBctGgRVqxYoVtEtsUgNIypQSibqc+cSVQZXaIkYxAaxtQglNdiOWZHZA8MQsOYGoSdOnXiHCHZDYPQMKYG4eDBgzF58mTdIrItBqFhTA3C06dPq4fIHhiEhjE1CH/99VcsX75ct4hsi0FoGFODUDZUc46Q7IVBaBhTg5DXeZI9MQgNY2oQyjnj3bt36xaRbTEIDWNqEO7fvx8HDhzQLSLbYhAaxtQg7NGjB4YPH65bRLbFIDQMF0uIko5BaBhTg3DOnDlYvHixbhHZFoPQMKYGYUhICEJDQ3WLyLYYhIYxNQhHjRqFadOm6RaRbTEIDcM5QqKkYxAaxtQglFvsRo8erVtEtsUgNIypQRgQEICgoCDdIrItBqFhTA3C1atXY926dbpFZFsMQsOYGoTdunXD0KFDdYvIthiEhjE1CDt06IBBgwbpFpFtMQgNY2oQymuxj4+PbhHZFoPQMKYGob+/v3qI7IFBaBhTg9DT0xPjx4/XLSLbYhAaxtQgbN++PecIyW4YhIYxNQgnTZqE+fPn6xaRbTEIDWNqEErRheDgYN0isi0GoWFMDcLZs2dj0aJFukVkWwxCw3COkCjpGISGMTUI+/fvj7Fjx+oWkW0xCA1jahDKxU1HjhzRLSLbYhAaxtQg/Oeff7Bt2zbdIrItBqFhTA3Cjh07co6Q7IZBaBhTg7Br166sPkN2wyA0jKlB+Ouvv2LVqlW6RWRbDELDmBqEp0+fxpkzZ3SLyLYYhIYxNQhlfpDbZ8heGISGMTUIu3TpgiFDhugWkW0xCA1jahB6eXlh4sSJukVkWwxCw5gahFJw4dy5c7pFZFsMQsOYGoRScGHZsmW6RWRbDELDcI6QKOkYhIYxNQi5oZrsiUFoGFODcPv27dizZ49ukauIjo5Wvxdv376te6yJQWgYU4NQQnDv3r26Ra7C19cX+fLlQ9myZTFu3Djs2LFDbYwPDw/Xn7AGBqFhTA3Cnj17YsSIEbpFrkJ+HzZq1Ahp0qTBk08+iaeeegrZs2dH3bp1MWHCBHVf9cGDBxEWFqZ/hHMwCA2zc+dOtGjRQrfMISdLJk+erFvkSmJiYlC9enUVhgk9uXLlQsOGDeHt7Y0FCxaokf/Nmzf1j3YMuwThmjVr0LZtW3Tq1ImPA5/OnTujdu3a6lWkXbt2CX7GVZ/SpUujfPnyCX6Nj7Wf7t27o2bNmnjiiScSDML4T+7cuVGxYkU0bdoUFy5c0KliX3YJwt27d2PkyJHqbCgfxz1y8kICsGTJkurXXy5ET+hzrvhMnz4d06ZNS/BrfKz7yLzgzJkz0apVK6RLly7B4It70qdPj7Rp0+Kll15CiRIl0KFDB4e9MvPV2DC3bt1SlVqIrOLixYtqsSR+8Ml8YdasWfHWW2+pEaPcXS2LKadOncKVK1f0j3YMBiER2Y0slri7u98NP3ntLVq0KGrVqoVRo0apOW1ZQZZtNs7EICQiu5G3kypVqsDDw0NN12zZssWSOxoYhAa5EXIY6xbPw7QpUzBrwXLsOnFZf4XIOWSkd+3aNd2yLgahEa5g86xuKPv+28iZKy8KFHwPb+fOiTffLYom3osR5NidCEQuh0Ho8q7j32nN8PoLL6GYhxfW+vrhZOBJ+B/ZgsmdqiDbsxnxZZ/fEWrtE06WJKcimjVrpuaxQkJCjNukTv9hELq46yeXoXrO55G//ggcj9Sdd4ViUafSyJDhQ4zeHqr7KLHkUvksWbKoLR05c+aEm5ub2tS9adMmHD161HLHxCj5GIQu7vi8b/BSxnfR6/dg3XO/W7unovTrz+LT3htwS/dR4i1fvhwZM2a8b9uHPHny5EHjxo3VyufixYvVMTFnr3xS8jEIXVoUNvYqgQxvfYHp+3RXfGEb0KRIVuSuMQERLvJ6HBN1E2FXwmL/66RxE9dvPvonHhgYiP379+PQoUN2eZo0aaJGhfHD8N6nYMGCqF+/vqqbKOXC5AytHC0j18AgdGmRWNOlKF7MWwFzD+uu+MI3onnRbHij6liEu0gQnts6B42r1kKXvl3h8fWnKPlpdXgu9EVCsSJnUuUcsuxLk8P9tn5atmyJqlWrqs2/CQXgw54PP/wQN27c0D9LsjoGoUu7jf0TayBDlsIYuvEh81XHF+CrPM+jUNvfY2PTNZxc5YX30qfBEzlKodOwyZg7dx7+2JXwfSVS5072qh07dgx+fn42ffz9/dVf69Wr99AR4TPPPIPMmTOrjcLyOZlD3LZtGw4fPmz5Gnz0Hwahi7tycCY+fflFlOiwEA9G4W1sHV0Xrzz7GrqtCtJ91he0djg+eip2VNV5GS7qPmeR8833Bp+ch33zzTdRpEgR1KlTR5WSkmopsnASFaVe5skFMQhdXdRlrOxTBhkyvIFGw1bg8NkwRMe+RF6/cAI+P3bDR5mewdv1xsM/3HXmqwLXeKPQU0/DbdZup45iJeAk/F599VVUrlwZzZs3x5gxY1S17MhIVxlfU2IwCA0Qc9Uf87pVw5uZM+HNj0qjavVqKF88P7JlzoFS7t7Ydsa15qpUED6dAR5zd8OZe8GDgoIwevRotV3GFU5HUPIxCI1xDUe2LMfkYf3QqX1H9BsyEUvW78F5FzxVcicIn4f7HOcGIaUeDEKynBMrByBv7Ctp7ek7GITkEAxCspzgf+ei0aef44eVR11mpZtcG4OQiFI9BiERpXoMQiJK9RiERJTqMQiJKNVjEBJRqscgJKJUj0FIRKkeg5CIUj0GIRGlegxCIkr1GIRElOoxCIko1WMQElEqB/w/v5Iwb1otn/kAAAAASUVORK5CYII=)
Figure below shows the variation of the moment of inertia of a uniform rod about an axis normal to its length with the distance of the axis from the end of the rod. The moment of inertia of the rod about an axis passing through its centre and perpendicular to the its length is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAUIAAADaCAYAAADT70sGAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACHwSURBVHhe7d0LfM/V/wdwl/p3VfklhBRFiZTKJZTkFiL3y7CVu+R+v4uZud/vd5EilGuExCJ3c79sY3OZmetsmM1e/72PMzHDLt/L53v2ej4en0eds6+S7OV8zuV90oCIKJVjELqAsLAw7N69Gzdu3NA9RGRLDEIXMGvWLOTOnRunTp3SPURkSwxCF9CmTRukSZMGvr6+uoeIbIlB6ALc3d1VEM6ePVv3EJEtMQgt7uLFiyhTpowKQg8PD91LJrp9+zZiYmJ0ixyJQWhxmzZtQrZs2VQQFihQAFFRUforD3f58mX1TUWuZdWqVVi/fr1ukSMxCC1u0qRJKgTlyZkzJw4fPqy/krDFixfj22+/RWRkpO4hV9GjRw/0799ft8iRGIR2sGbNGhw6dEi3UqZ79+53g/C5557D9OnT9VcS1rBhQzz77LMIDQ3VPeQq+vXrBy8vL90iR2IQ2kGrVq0wb9483Uq+8+fPo3LlyneDUB4Z7T3Kl19+iSeeeIKvWC6IQeg8DEI7kO0uM2bM0K3k2759O1555ZX7grB06dKIjo7Wn7jflStXULhwYfU5vmK5Hgah8zAI7aBPnz4YN26cbiXfkiVL7gtBed59992H7if8+++/kSNHDvU5GUmSa2EQOg+D0A5GjBgBb2/vh47cEkN+7MCBAx8Iwqeffvqh84TDhg1DunTp1OdkZHjp0iX9FXIFDELnYRDagQRV7969cfPmTd2TdLJ/sHz58g8EoTwdO3bUn7pfs2bN7n5GttzIog25jr59+zIInYRBaAeLFi1Chw4dEB4ernuSzt/fHy+88IIKNVn8kJXg9OnTq3bt2rURERGhP3mHLKxUqFDhbhCmTZsWnp6e+qvkCuQPuKFDh+oWORKD0A7Wrl2L5s2bq6oxybVw4UIVaLly5ULXrl3RqFEjtGzZEhkyZECWLFmwdetW/ck7ZH4wa9asd4NQnsetMJO1yO+ZCRMm6BY5EoPQDrZt24YGDRoke45OToXIyvOHH36oVo4PHjyIpk2bqlGfjDYLFSqEBQsW6E/fMW3atPtCUJ6yZcsiODhYf4KsTv4fz507V7fIkRiEdnDkyBFUq1Yt2Zua5bzpnj177m7K3rFjhzpnHBISotpnzpxRc4hxJDh79er1QBBmypQJ69at058iK5P5ZJnjlZNB5HgMQjs4d+6cGo3JX21BRoUShGfPntU995N/z8MWViZOnKg/RVZ24cIF9Wq8evVq3UOOxCC0g+vXr+Ozzz5DYGCg7kmZxwXhzp077y6syPaZuEUVebp06cKKJi5AFsdkRPjPP//oHnIkBqEdSIUYOeq2f/9+3ZMyjwvCX3/9VYWehKEsqsjosFixYqqvaNGiCAoK0p8kq9qyZYsaER4/flz3kCMxCO1ANkPLFpfNmzfrnpR5VBBKlZm6deuqEJT5JR8fH3z33Xcq/GSVWbbd8HXL+uQUkQRhSrZcUfIxCO1AXkVbt26tVnht4VFBKBc6jRkzRo0KhWyj+eabb9TfywT8Tz/9hICAANUm6xo/frwq1kHOwSC0E9kYa6vNsY97Nb7XX3/9pYIw/oZrsjYpksFCGc7DILQTGQ3Kq6ktJCcIZcGGXIP8oSWLWnJbITkHg9BOJLxkwcQWK7YMQrOdPn1azetyz6fzMAjtRBYrZPU2MeH1OAxCs8nuArmp8NixY7qHHI1BaCdy8kPO+m7YsEH3JB+D0GxyQZecROL/M+dhENrJrVu3MGDAAFWbMKUYhGaTFX/ZAkXOwyC0I7m3RF55UopBaDbZOiMVhsh5GIR2JMelatSooe4SSQkGoblkr6cU8Z08ebLuIWdgENqRbGRu3Lhxis+PMgjNJXPJUrJN5gnJeRiEdiSnPqTqcEr/tGcQmuvo0aMoU6YMLl++rHvIGRiEdjZ8+HC0a9dOt5KHQWiuZcuWqREhOReD0M6WL1+uttHcW0g1qeIqXktB1sdhELoWuaxJbh8k52IQ2pmfn58Kwvh3jCTFrl270KJFi0SV3WcQupZ69erxtkELYBDamZTkkgWTOXPm6J6ku3r1qgpDmXN8HAah65Cpji+++MJmBXwp+RiEDvDDDz+oy7tTcuF7YjEIXcePP/6oyrUl5g84si8GoQOsWLFC1Zqz1R0mj8IgdB1STVzCkJyPQegAsshRvXp17N69W/ckQcxtVfr/dkxM7N9GIfKW/L3+WgIYhK7hxIkT6nzxvn37dA85E4PQQerUqZO8itXh57BzxSR0auGBhk07YsqK7Tj3iIxjELqGqVOnom3btggLC9M95EwMQgfx9vbGwIEDVTGGJIkdEcacWIBKb2bA61VG4sQNjghdncwVN2nSBJMmTdI95GwMQgfZuHEj6tevr1aAkypi4xAUzpEVjeY8vl4dg9D65HVYfi/IJf5kDQxCB5EALFeuXDLmCaPw1+CayJH9c/x47PE3nDEIrW/cuHFqX6jcQEjWwCB0oGRd0BN9BIOq50X2Mp7wi3h82X8GobVJJSIJwZkzZ+oesgIGoQP5+vqibNmyuHDhgu55vNtHfkH1vP9DGa+/kZh76RiE1iYnjGS1+NSpU7qHrIBB6ECycVb2E8qKYeLE4PDPnZD3f/nhvenxBRcEg9C65CKvsWPHqouayFoYhA62dOlSVaw1cacJQrGg4yd4uWAr+JyN0n2PxiC0LnktlorlssGerIVB6GByvtTNzS1xB+0vbEWHopnx4fc/ITiRp/MYhNYl58XlZsNr167pHrIKBqGDyevR4MGD0b59e92TkBjcjo5CwOoBePuJTPh2+jbciu1LDAahdY0aNYp3k1gUg9AJZE+hjAofWnUkJhx+PkvQ3/0TZH81H9x6TsGuMxGJikIGoTXJMUlZJFm/fr3uISthEDqBHKuSsJo/f77uiS8GUZHXEX4tDOEREYi4fgO3ojkidGVyb02lSpVYkt+iGIROMnToUHWfia031TIIref27duqJqVspJapEbIeBqGTHDt2DFWrVlUT6LbEILSe1atX4+uvv07UVQvkHAxCJ+revTt69Oih5o9shUFoLbJCLOX4Z8yYoXvIihiETiSnC6RUu9xSZysMQmuReeDatWsn6TQROR6D0MnGjBmDpk2b2mzuiEFoHefPn0fdunWxYMEC3UNWxSB0stDQUFSsWBF//PGH7kkZBqF1zJs3T40GIyISc0qcnIlBaAHyDSOl/G1RrZhBaA2yTUZCcPHixbqHrIxBaAEyoS4X+ciB/JRiEFrDL7/8glq1arHmoItgEFqEBFjlypVx4MAB3ZM8DELnk1dh2S7z+++/6x6yOgahhXTr1k1tsk7JdhoGofPJxmkPDw/eV+xCGIQWEhAQoI5hrV27VvckHYPQufz9/dWVDHKkjlwHg9Bipk+frrZcJLdUE4PQeWQLVOvWrdG3b1+bbpIn+2MQWszNmzdVEEogJgeD0HlWrVql5nn9/Px0D7kKBqEF+fj4oEyZMggKCtI9iccgdA45RyxboGbPnq17yJUwCC1IXrF69uyJDh06JPnECYPQ8eT/kZwZl/topNIMuR4GoUVJ0VY5cSKbrZOCQeh4v/32myrBf/LkSd1DroZBaGFSzViKMuzYsUP3PB6D0LEk/CQEV65cqXvIFTEILU72pMnm3MTeg8sgdJxbt26pgqt9+vTRPeSqGIQWJ99s7dq1Q5s2bRK1QZdB6DjDhg1TK/wXL17UPeSqGIQuQL7R5OIfGR0+DoPQMeT4XNmyZbFnzx7dQ66MQegi9u7dq+YL161bp3sSxiC0v8OHD6sQXLJkie4hV8cgdCE///yzmpiXY1wPwyC0r9OnT6NGjRrqbmoyB4PQhcgetX79+qFBgwa4cuWK7r0fg9B+zp49q+YE5a4ZFlQwC4PQxYSHh6uVyk6dOiV4npVBaB8SgnIJE0PQTAxCFxQcHKxez7y8vHTPfxiEtie/3nXq1FEhKGfByTwMQhd15MgRVKhQ4YHiDAxC25IzxFJpmiFoNgahC/v333/VSrIsosRhENqOhKCMBKVgLkPQbAxCFyfbaT7//HN1R4b4+++/GYQ2EDcn2LVrV84JpgIMQgOsWbNGheGiRYuwbds2NGnShEGYAlIpXEaCDMHUg0FoCLkX+csvv8T333+P5s2bIzo6Wn+FkmLXrl3quoT+/fvzBrpUhEFoEKlS8/HHH+ODDz5Q9+pS0sjIWgriTpw4UfdQasEgNIRcJL59+3ZVDipnzpxq0/Xx48f1V+lxZPU9bnqBUh8GoYuTkZ9cFvTkk0/C09NThZ+bmxu6dOmi7s+QV2Z6uLCwMLU1Rl6HN23apHsptWEQuig5bichV7x4caRJk0a90oWGhqprJJs1a6bmCGV0I/1SLoqT/g+S4gmyMty0aVNWl07lGIQuSL5pZVHkxRdfVCGYJUsWbN68WX1tw4YNavuM1DEU+/btUyugspLM29X+I+X15f5hKZ7AFXZiELoQOWcst6QVKFBABaA8adOmVa92cRLaUC2vf1JFWe5AidtvmFpdvXoVAwcOVFV8li5dqnsptWMQugh55ZUFkLgAjHuKFClyX4XkR50skQUVmQuTitep8VVQiqjKr2HDhg3VazFRHAahxcliyA8//KBWguOHYPr06R8Y1TzuiJ0EYOfOndWewx9//DFVHB07ceKEOiYn/83e3t5qhEx0LwahRUlALVu2DCVLlnwgAOOeuEWReyXmrLHcwytzZDI6ktfl0aNHq/nDuHlFU0joS/1GqSbdu3dv7Ny5U3+F6H4MQguSECtcuHCC4Rf3vP766zhw4ID+Ef9JStGFS5cuqbPJ7du3V2EhF8pv3brV5U+lBAUFYeTIkWrFXI7JyTUHPGlDj8IgtKCIiAhVCVkeGfXlzZv3vhB86qmnMGHCBP3p+yUlCOPICFEulJcVVHl9jAsPVxMSEoKZM2eiSpUqaksMR4CUWAxCi5MCAPXr10e+fPnUnKAEoSx4XLhwQX/ifskJwnvJK7LMp3311VfqvK2Pj4+lR1NyZYGcppGfq/w6yb5AmVIgSgoGoYXt3r1bFV+dOnUqhgwZgnTp0iFr1qxYv369/sSDUhqEceSUhYwMGzVqhJo1a6JXr16q5Ne1a9f0J5xHiiGsWrVK3fUsPzfZI9mjRw+1gVxG00RJxSC0KKmCInvdxo4dq9qyf1BGgzKf9yi2CsI4x44dUyMuWW2VUJS5RA8PD1WYQEp+yYgsobtTbEVOxMi/Q+50llHf+PHj1eu7LPTIIo/890oBVaKUYBBakMzPyTe7fPPL/J2QbTKlSpXCqVOnVPthbB2E95I5uP3796tN2TICk7PM8siK7MKFC9VCi3xdtqvIZ2UDeFJI6Mkrv7yeyyLOpEmT1J5HuZ8lU6ZMyJMnj9pKJKPV8+fP6x9FlHIMQouRI3HyOiwheC95HTx37pxuPZw9g/BectZZgks2KY8ZM0ZtUpYRbLVq1eDu7o7WrVursJQFGBnVyuLOwx4Z5Q0dOlQFatu2bdU8nwSsjH4ldOUPBumXM9NxfzAQ2RKD0EJ8fX3V+de41+HkcFQQPoyMBCW4ZA5vxowZ6jibhJgE48MeOTctRwBlBCgjX/l1iB94Bw8exNGjR3WLyLYYhBYhIysJQZn3SglnB6G9yGu3FJ4lsgcGoQVICMqc4KhRo1L86mdqEMqWHlk5J7IHBqGTyZxg3DE3W8x/mRqEHTt2TPBCeyJbYBA6kRyRk4WRlL4O38vUIJRV6RUrVugWkW0xCJ1EtpnIKqu8DtuSqUEoK+bBwcG6RWRbDEInkBMjEoJSGMDWTA3C4cOHY8qUKbpFZFsMQgeTyijVq1fHiBEj7LInztQglMo4nCMke2EQOpgUWv3333/VhmR7MDUIZcVYzlwT2QOD0DCmBqGcJz59+rRuEdkWg9AwpgahnDhZvXq1bhHZFoPQTmLCjmPJ+P5o36EXpq/eh6SVH0g+U4OQ+wjJnhiEdhGBdSOboWHncVj68xg0b9ASk9cHwBHlAkwNwp49e6oFJiJ7cE4Q3r6FqCSsFUTfikTUI1MkBtFRsf/MpPxD7en2FWxZPB8bg6QRionN3dB5sg9uqC/al6lBuGXLFp41JrtxbBBGXcau3yeiS4tv8W3Lbpiyci8uPaKm59WgXZg/rDuaf+OBJm36YMaqvbic4Ocv4I/Jnhg0fQOcXz9Z/JfaQWtGwq1eGyzcfYEjwhSQDehSgYbIHhwXhNFXsXm8O97KnhvlGrRCy/pl8UbWvGg8wQdX9EfuFea3Et+VzInsBcuiWeu2aFmrJHJkzg23kX/h6gO3Tvqj/5d5kOfroQjRPc4XjeN/jEKjWh4Y88dh2K+G8/1MDcLu3buz6ALZjcOC8NrRRaia62WU7vG7fkUMx9LupZA5bw0sPBb/pfEylnT5DM9nKo05vnHf0Jcxr01RvPBaNfzmF/9eigB4Vs2P/DVH4m7d4ujruHDuDC5cuyeCoiIQduPORUTREVdxJfwmEvcyHY3rYVdwLfJOK/LaVUTcm2wxkQgLu/fnFIOAdWPgXr8lZm09q/scw9QglPtTpHgrkT04KAijcOCXlsieuSQmbA3TfbHRtmcyir6aG23mxr+f9wq2LxmPYbM24co9F6j5zmyGHBk/xqQ98W9wkyAsgAK1RsXGZayLOzC4cTmUcfPEtkuxL6TXA7BgYFOUKVEcn5QohyYd+qNPCzc09lr6X3A+yq1jmN7ZHS17eaNve3eULl4MxUpWg9ciH2xZMQXNKpdEsWLFUO5bT2w8KcNVf3hXfQeZc3+Cet+4ocbXrTDDx98ho0JTg1CKvEq1aiJ7cFAQhmOTd3lkfrculhzXXbFu+K9F7dyvoNrQtQksJMSbUYvwRb+vXsf/inbEjpD410tKEL6HQg2n4PLl/Rjp8TGyvVMF49cH4nrUZfzWuzxeyfIevu0/FQt/HIfvK7+Lp9OkwYdNJyNRW3Qj96B/pTeQ5v9eRZWOI7FwyVx0/vo9vPjcy3j3C3d4TpqP+WM74P0XX0CZnksQEnMd50764diRQ9jvuxd79hzC6csRnCNMAbmjhPeUkL04KAjD8GfvkshcyAOr1ErqHVGBG+GeJxMq/LAcV3VfgmJHdDPafIaMGd/HDyuOxr6oxncCg2sWQv4vvkXX+oWQrUAtzNl7UX3l+vFFqPhaFlQd+Aduqp7YTPVbiq8zZ0CRltORqPvPIvdhYLVceL5QO+zSg9HAPwYgX7pn4DZ1G9SUZUwgJtbOhRyVB+GAEzPI1CCUKj08Ykf24qAgvIYNA0oj8/sNsfyE7ooVeWIDGryZCZU8Vz50tTc6ZBeGexRBxkwF0W3BTiT87R2IETXz4f+eSIM0adLitc864p8rd8Zfpzb0QN7MH2HAqnuWUW6cxLCK76Jw0ykPBGHogbUY3aurmpPq2rUbvGduwuWow/Cqmgv53KbjrF6oOfPnMHyc7W30W3PyTkf0acxuXACvVxoIX0ftnk4A5wiJks5BQRiJndPqIXuurzB/338zZdcOL0L517Kj0fgtCYzyZIFlNTpUeAsv5y6HkWsSGgnGOanm5LIVqo2xUwejXM6M+LTLb7Hj0Nhg8+mNPJkLod+Ke2rZXT+JoRXeSTAIT6ybgFofvYN8+fMj3zsFUKH5NJyNPoohX+dGQffZOKMXTE6tGYKPYoOw7+qAOx1RQZj5TX68UdkT+xiENic33HFDNdmLg4IQCP5nFD7O/CbaLziie4Cji77Da1mLYtj6UN3zn5v+a9D2i9fw6kffYNG+S7r3YQIwsEoBFHSbipjYuNw8vDpezpAPAzcGI/LcWtTIlRnle94JRnHt6EJUyvQ8irR48NU46vpVhJwOROCpUwgKPIXg0HDERO6P/efnwnuNZjEInSQgIACBgYG6RWRbDgvCmGuHMap+fmTOXwMTVmyFz2+jUPntzPig/nAclnAJ34ERHVqhx/TtsaFyCjNbfBD7mpsGheu2g9ewIRjQrx/69umNvoNmYse5+Enjhz5l34gNIW+oSA3fhZ5lsuG5dzyw1v8sNo6qh5yvvoM6Hb0wcZw3mld6DxnSP42SrWcmbo7w5h70KpMJuWpNxSkdhIErB+DtDNnRbbnfnY6ok5hc93W8XLoP9jhxV7epQfjnn39i48aNukVkWw4LQhHhvw79GpTGB+8XxHvvvY/SDfpiXYBeL768EZ1rVIL7kL8Qc9EXI1qUQ7FPSqLU56XwaYkSKCFP8eIoUbY1fjsef4R4FrO7NkTDXj8j7iuhmyaiXvky6PyTjEAjsHlmD1Qr8xlKVayLzv2Hwf2jHCgRG4SPvzI91i0/zOpaC40GrESoniMM2TYPjavWw7S4fYLRIVjh2QA1O8+GnxMzyNQglA3VcsE7kT04NAjviETIyaM4EnAu9u/s7/YVPyyaMgV/3ZtOl/5GrTxZ8WWfFQ45/+tIpgahVKgeNGiQbhHZlhOC0LFuX/ZF15IZ8UKB2hj70+9YuXQeetf/CJlylcOkf+NvzHZ9pgbh2rVrsXnzZt0isi3jg1COx108sBw93SuieLHiKF68BEp91RgT1xx2WI1ARzI1CI8fP45jx47pFpFtpYIgvCPmxiWcPuGH4/4nEXI1bmu1eUwNQk9PT4wfP163iGwr1QRhamFqELZv355zhGQ3DELDmBqEEyZMwLx583SLyLYYhIYxNQiDg4Nx9qxjS5pR6sEgNIypQTh79mwsXLhQt4hsi0FoGM4REiUdg9AwpgZhv379MGbMGN0isi0GoWFMDcJDhw5xHyHZDYPQMKYGoVznuX37dt0isi0GoWFMDcLOnTvDy8tLt4hsi0FoGFODsEuXLvD29tYtIttiEBrG1CBctGgRVqxYoVtEtsUgNIypQSibqc+cSVQZXaIkYxAaxtQglNdiOWZHZA8MQsOYGoSdOnXiHCHZDYPQMKYG4eDBgzF58mTdIrItBqFhTA3C06dPq4fIHhiEhjE1CH/99VcsX75ct4hsi0FoGFODUDZUc46Q7IVBaBhTg5DXeZI9MQgNY2oQyjnj3bt36xaRbTEIDWNqEO7fvx8HDhzQLSLbYhAaxtQg7NGjB4YPH65bRLbFIDQMF0uIko5BaBhTg3DOnDlYvHixbhHZFoPQMKYGYUhICEJDQ3WLyLYYhIYxNQhHjRqFadOm6RaRbTEIDcM5QqKkYxAaxtQglFvsRo8erVtEtsUgNIypQRgQEICgoCDdIrItBqFhTA3C1atXY926dbpFZFsMQsOYGoTdunXD0KFDdYvIthiEhjE1CDt06IBBgwbpFpFtMQgNY2oQymuxj4+PbhHZFoPQMKYGob+/v3qI7IFBaBhTg9DT0xPjx4/XLSLbYhAaxtQgbN++PecIyW4YhIYxNQgnTZqE+fPn6xaRbTEIDWNqEErRheDgYN0isi0GoWFMDcLZs2dj0aJFukVkWwxCw3COkCjpGISGMTUI+/fvj7Fjx+oWkW0xCA1jahDKxU1HjhzRLSLbYhAaxtQg/Oeff7Bt2zbdIrItBqFhTA3Cjh07co6Q7IZBaBhTg7Br166sPkN2wyA0jKlB+Ouvv2LVqlW6RWRbDELDmBqEp0+fxpkzZ3SLyLYYhIYxNQhlfpDbZ8heGISGMTUIu3TpgiFDhugWkW0xCA1jahB6eXlh4sSJukVkWwxCw5gahFJw4dy5c7pFZFsMQsOYGoRScGHZsmW6RWRbDELDcI6QKOkYhIYxNQi5oZrsiUFoGFODcPv27dizZ49ukauIjo5Wvxdv376te6yJQWgYU4NQQnDv3r26Ra7C19cX+fLlQ9myZTFu3Djs2LFDbYwPDw/Xn7AGBqFhTA3Cnj17YsSIEbpFrkJ+HzZq1Ahp0qTBk08+iaeeegrZs2dH3bp1MWHCBHVf9cGDBxEWFqZ/hHMwCA2zc+dOtGjRQrfMISdLJk+erFvkSmJiYlC9enUVhgk9uXLlQsOGDeHt7Y0FCxaokf/Nmzf1j3YMuwThmjVr0LZtW3Tq1ImPA5/OnTujdu3a6lWkXbt2CX7GVZ/SpUujfPnyCX6Nj7Wf7t27o2bNmnjiiScSDML4T+7cuVGxYkU0bdoUFy5c0KliX3YJwt27d2PkyJHqbCgfxz1y8kICsGTJkurXXy5ET+hzrvhMnz4d06ZNS/BrfKz7yLzgzJkz0apVK6RLly7B4It70qdPj7Rp0+Kll15CiRIl0KFDB4e9MvPV2DC3bt1SlVqIrOLixYtqsSR+8Ml8YdasWfHWW2+pEaPcXS2LKadOncKVK1f0j3YMBiER2Y0slri7u98NP3ntLVq0KGrVqoVRo0apOW1ZQZZtNs7EICQiu5G3kypVqsDDw0NN12zZssWSOxoYhAa5EXIY6xbPw7QpUzBrwXLsOnFZf4XIOWSkd+3aNd2yLgahEa5g86xuKPv+28iZKy8KFHwPb+fOiTffLYom3osR5NidCEQuh0Ho8q7j32nN8PoLL6GYhxfW+vrhZOBJ+B/ZgsmdqiDbsxnxZZ/fEWrtE06WJKcimjVrpuaxQkJCjNukTv9hELq46yeXoXrO55G//ggcj9Sdd4ViUafSyJDhQ4zeHqr7KLHkUvksWbKoLR05c+aEm5ub2tS9adMmHD161HLHxCj5GIQu7vi8b/BSxnfR6/dg3XO/W7unovTrz+LT3htwS/dR4i1fvhwZM2a8b9uHPHny5EHjxo3VyufixYvVMTFnr3xS8jEIXVoUNvYqgQxvfYHp+3RXfGEb0KRIVuSuMQERLvJ6HBN1E2FXwmL/66RxE9dvPvonHhgYiP379+PQoUN2eZo0aaJGhfHD8N6nYMGCqF+/vqqbKOXC5AytHC0j18AgdGmRWNOlKF7MWwFzD+uu+MI3onnRbHij6liEu0gQnts6B42r1kKXvl3h8fWnKPlpdXgu9EVCsSJnUuUcsuxLk8P9tn5atmyJqlWrqs2/CQXgw54PP/wQN27c0D9LsjoGoUu7jf0TayBDlsIYuvEh81XHF+CrPM+jUNvfY2PTNZxc5YX30qfBEzlKodOwyZg7dx7+2JXwfSVS5072qh07dgx+fn42ffz9/dVf69Wr99AR4TPPPIPMmTOrjcLyOZlD3LZtGw4fPmz5Gnz0Hwahi7tycCY+fflFlOiwEA9G4W1sHV0Xrzz7GrqtCtJ91he0djg+eip2VNV5GS7qPmeR8833Bp+ch33zzTdRpEgR1KlTR5WSkmopsnASFaVe5skFMQhdXdRlrOxTBhkyvIFGw1bg8NkwRMe+RF6/cAI+P3bDR5mewdv1xsM/3HXmqwLXeKPQU0/DbdZup45iJeAk/F599VVUrlwZzZs3x5gxY1S17MhIVxlfU2IwCA0Qc9Uf87pVw5uZM+HNj0qjavVqKF88P7JlzoFS7t7Ydsa15qpUED6dAR5zd8OZe8GDgoIwevRotV3GFU5HUPIxCI1xDUe2LMfkYf3QqX1H9BsyEUvW78F5FzxVcicIn4f7HOcGIaUeDEKynBMrByBv7Ctp7ek7GITkEAxCspzgf+ei0aef44eVR11mpZtcG4OQiFI9BiERpXoMQiJK9RiERJTqMQiJKNVjEBJRqscgJKJUj0FIRKkeg5CIUj0GIRGlegxCIkr1GIRElOoxCIko1WMQElEqB/w/v5Iwb1otn/kAAAAASUVORK5CYII=)
physics-General
physics-
Two thin rods of mass
and length l each are joined to form l shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod and perpendicular to both the rods is:
![](data:image/png;base64,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)
Two thin rods of mass
and length l each are joined to form l shape as shown. The moment of inertia of rods about an axis passing through free end (O) of a rod and perpendicular to both the rods is:
![](data:image/png;base64,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)
physics-General