Physics-
General
Easy
Question
A block of mass 12 kg is attached to a string wrapped around a wheel of radius 10 cm. The acceleration of the block moving down the inclined plane is
. The tension in the string is (I of wheel
kg
)
![](data:image/png;base64,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)
- 24.5 N
- 68.7 N
- 23.4 N
- 46.8 N
The correct answer is: 23.4 N
Related Questions to study
physics-
' O ' is the center of a square ABCD.
and
are four forces acting along the sides AB, BC, CD and AD as shown in figure. What should be the magnitude of
so that, the total torque about 'O' is zero ?
![](data:image/png;base64,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)
' O ' is the center of a square ABCD.
and
are four forces acting along the sides AB, BC, CD and AD as shown in figure. What should be the magnitude of
so that, the total torque about 'O' is zero ?
![](data:image/png;base64,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)
physics-General
physics-
A cylinder of mass M and radius R starts falling under gravity at t=0 as shown in figure. If the mass of chord is negligible, the tension in each string is
![](data:image/png;base64,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)
A cylinder of mass M and radius R starts falling under gravity at t=0 as shown in figure. If the mass of chord is negligible, the tension in each string is
![](data:image/png;base64,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)
physics-General
physics-
A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m. On releasing from rest, the block falls through 5 m height in 2 s. The M.I. of the wheel will be
![](data:image/png;base64,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)
A block of mass 2 kg hangs from the rim of a wheel of radius 0.5 m. On releasing from rest, the block falls through 5 m height in 2 s. The M.I. of the wheel will be
![](data:image/png;base64,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)
physics-General
physics-
A rod is free to rotate about 'O' as shown. It begins to rotate. When it has turned through an angle '
' its angular velocity 'w' is given as
![](data:image/png;base64,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)
A rod is free to rotate about 'O' as shown. It begins to rotate. When it has turned through an angle '
' its angular velocity 'w' is given as
![](data:image/png;base64,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)
physics-General
physics-
As shown in figure, a stick half of which is made of wood and other half of iron is pivoted as shown in fig. (A) It is pivoted at wooden end and force is applied to the other end of it at right angles to its length. (B) It is pivoted at iron end and the same force is applied to the other end at right angles to its length. Then angular acceleration produced is
![](data:image/png;base64,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)
As shown in figure, a stick half of which is made of wood and other half of iron is pivoted as shown in fig. (A) It is pivoted at wooden end and force is applied to the other end of it at right angles to its length. (B) It is pivoted at iron end and the same force is applied to the other end at right angles to its length. Then angular acceleration produced is
![](data:image/png;base64,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)
physics-General
physics-
' O ' is the centre of an equilateral triangle ABC
and
are three forces acting along the sides AB, BC and AC as shown in figure. What should be the magnitude of
, so that the total torque about ' O ' is zero ?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALkAAACCCAYAAAAaEGkyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABTVSURBVHhe7Z0HWNNX98epe79q3b5qrdZW1KrgqIpbQX31rxbrrnWDIi6KVsW6V7W2/t0KalEQVIqrLlBEBUFALKiIA9ngYInICnzfnMsvMgovARKS/HI/z3MfzckvgZBvbs4995xzdcDhiBwuco7o4SLniB4uco7o4SLniB4uco7o4SLniB4uco7o0VqRB7kcw46j14RbHDGjpSJPxSbjNqjxxTi8SBNMHNGilSJPCXaGbjUd6OjUxZaLzwQrR6xoocgzYb9hJgYMMkLzyjpoZ7wB77KFuziiROtEnhHtjm8NjeEWFIQlA5tAp3JbnH6UKNzLESNaJ3LX30ww0nQXaPK+d9BU6rLoYNhyB3abI060S+QfnmLOKCMcuPMq53a8LwY3q4RKLYfC97Ukx8YRHVol8uBzG9Gj/xTcC4tFZGQkoqPDsOV7PelsXgmLj3kLV3HEhhaJ/D02TzNAx77fYumSRVhgZoaFiywwd5IRakhdlqb9zBHDJ3NRojUij/OzxeAh43E7JA4J8fGIi4tDXHwCEuNDsHhgc+ls/in2uEcLV3PEhJaIXIIjluMxa/M54XZ+Hjr9jNrS2Vx/+u/ge0PiQytEHnvPFh2btcEBn3jBkh9JyA3o16LNoabYc/0Zj7SIDNGLPMzvL8wfOxC6uvr4wWIjbjyMEe7JIe3VE1hvWoh+3Tuho+6XMBgxBUcu+nChiwjRi1ySmY7U9Ez2//TUD8jIzGL/l5GdJUFqatpHUUsy0j5ezxEHWrPw5GgvXOQc0cNFzhE9XOQc0cNFzhE9XOQc0aP1Ik9LS8PYsWPRo0cPXLx4UbByxITWi/zChQssp5xGs2bN8Pz5c+EejljQapFnZ2djwoQJTOA9e/Zk/xoYGCA5OVm4giMGtFrkT548QdWqVdG2bVtER0dj0qRJTOimpqbCFRwxoNUi//nnn5moly9fzm7HxMRAV1eX2fbu3ctsHM1Ha0WekJCANm3aoEqVKnj06JFgBe7du4datWox+40bNwQrR5PRWpGfOnWKzdjGxsbMN8/L8ePH2X2ff/45Xr58KVg5morWitzQ0JAJ2dnZWbDkx9LSkt0/dOhQfPjwQbAqAOkHKjMjQ7jBKQ+0UuR+fn6oUKECvvjiC6SmpgrW/GRIhWhkZMSEvnjxYsGqAD5E49LJQ7CYNxNTp07FLNMFWLZsGftQWVpawGTGBIwcMwPnAngpnqLQSpEvXbqUiXfbtm2CpXCoov/LL79k11pbWwvWspKNLEkqLm2ZzJ63g/Fq3Pf3Zx88Pz8fXDtnjSEd2mDhMU/hek5Z0TqRv3r1im361K5dG8+eFd8H8fbt26hevTpbjHp6Kk54sS7bUVEq8oFL7ARLLqFujrA+f5dXJykIrRP54cOH2Qw6ZcoUwVI8Bw8eZI9p3749oqKiBGvZCL+8FZWlz9l/4THBkgNbA0sykPIht1qJUza0SuTkZ/fq1YsJ9vr164JVPhYuXMgeN2bMGJbvUlZI5JWkzzdoqb1gId7B9YoLYpKEmxyFoFUiv3nzJhNq9+7dSyzU9+/fY+DAgezxq1atEqylh0ReTfpcehPXwV/qk/v7+8HVbgvGTrPEy3fCRRyFoFUinzVrFhPpnj17BEvJIB/+3//+N3uOkydPCtbSEX55G+v10ki3P0znzcc809kYoNsQTfvOwyteR61QtEbk4eHhbPHYoEEDtn1fWq5evYpq1arh008/ha+vr2AtOTKfvK+ZNdLT06UjDcnht7Bi1Va8iC/EG095BZc/7WB/9jreFB715BSB1oh8+/btbAaeP3++YCk9v/32G3uuLl264M2bN4K1ZMhEPmCRrWAh3uO+jx/eJuZvm5GaGIK9VvPx7X8M8VXLRug2bhXCPvDGjfKiFSInf7pr165sA8jbu+zdaykNYMaMGUzolKqblZVflPJQVHSlMML9r+PCrcfs/6HXd6BBhQb43SOC3eYUj1aI/NKlS0yQgwYNQmamYhzexMRE9O7dmz3vpk2bBGsu5L8fPXq0yNyXyKu/5Mzki/PO5IWTlZXHfUm4izF9jXDuKT8dQ160QuTjxo1jYrS1LV5QJYGyF5s2bYqKFSvi7NmzgjUHGxsb9jPNzMwES35CnVez+7vN3i9Y5CA9EU6/LYPVIVfBwJEH0Ys8KCgINWrUQPPmzVl6raKhBC8Sa6NGjfD4cY5LQYSGhqJy5cqsICNfglfqa9w4a4s5I/TYArZxOwOsO3ACgeHFzMxpb3Fh33K0qvEJWvWYgruhPM4oL6IX+fr165kIraysBIvi2bhxI/sZVAxNbowMWaaju7u7YJEiSUVsRAiCnz5nuTFhIc/w5GkIElKKyUyUpOF1TBT+vmGLr+tWQl/zY+BLT/kQtcipVvOzzz5juScBAQGCVfFIJJKPtaI//PCDYAX27dvHbGvWrBEsisFhzVh0HrYcCkwAFjWiFjlt2JDIRo0aJViUx+vXr9GpUyf283bs2MFsDx8+ZB8wfX19FgtXFI6bZmLOBifhFqc4RCtyCusNHz6cie7cucJPmCgNFBenErnCePDgAerVq8cWorRpRMgiMGX5JvE8sRnTzVbigusNuDhZw3LFFjyI5YUX8iJakVN+NlXiU2Hyu3eKW6Rt3ryZiXb06NEsF6YgDg4O7H7a/qeMxd27d7PbW7duFa4oOSFezvhxwRwsXrkBRxwuIOSt4r4VtAHRipyqeUhchcWwywLN1rNnz2YbS/T85Aq5uLgI9+awYsUKdt+IESNw9+5d9mGj5C7y3TnljyhFTv5xkyZNmD8cEhIiWBVLYGAgSxGgMCAJetiwYR9dFIIKpMlOSWGU3luzZk3W54VT/ohS5LLCiGnTpgkW5UGLSxI7tbCgnzl48GBcvnwZsbGxLKRI/jnFyuk+xZXQcUqC6EROLgEt9sidKOhGKJPg4GAsWbKEbTyRoEeOHImVK1eyMju6TYMWwgXbX3CUj+hEfuvWLSaobt26sUqg8oZyVqjyntwT+j1kMzwNcluK6g7AUR6iE/n06dOZoFTd5u3Fixes/Rx16aLaUPqdaCZPSUkRruCUF6ISOeWLUFFEw4YNWQPP0uLo6Mh6llNjoZ07d7JU3dJCcXUKJdJzkdAtLCyEe9SDrJQ38L1zE+537rKwq7fnHRYalQ136Tejl08g4j5obrmSqEQuK2YoKvNPHig9lp4j71iwYEGZw39hYWEfF6D0M9SFrJTX8L7hDJPhndn6oduw77F27RpYWa2G1aqfMG1sH9T7V1sc8IoUHqF5iEbktG3esWNHJiKKTZeWvn375hM4DcowJJGWFWogSmHNunXrwsvLS7CqB/cPm7DXOn5j/tM2JKmx2G46CVucHwgWzUM0IqejUOhNGjBggGApHbLWE3kHRWsUtWsq2wGlndiyuFSK5qGdBfu9Jm3+S7Dkkhz6EH7BfCZXOePHj2dv0okTJwRL6aAOW9SMn4qeKRxIM/v9+/eFexUDNfmn35X8fkUmbpWFgOM5rfMmbsor8jRER8VqfEqvKEROMWoK1VFa7du3bwVr2aBQIG30KEOESUlJ6NevHxOVMvPcS4JM5JO35e7a4u09bN1+GK81PKdXFCKnZj/0BlF3WE2BtvipdI5+77L2cFEEASd+ZL9L+wETpQvPtVhj9RNGf9MGXxuvgaYHPTVe5PHx8SxqQTM5zbyaBBVYU4lc/fr1Fe4SlZSA4zk+ea8Jy9kBBacc7LF10XcYOn0DkkrejECt0HiRy1JbKfVVE7fMZf1g9PT0EBcXJ1jLH5m78v2OvEfIvMQRG0e8KWSbIP3tM+y0nIG+vftgktla+EWobwNHjRc5JUTRm+PkpJmVMlTcQc346TVQCZ2qPqi5C8+8IcQM6TdlIjILrjzTX+Hw6rmYZr4Gh3dvxDdNK6Nxn9l4mqCeU75Gi9zHx4clYrVr106jt8upiwA1ISWRKTr/XV4KF3nhvA9/hLN/3YBsSR7jtgN1qjbBHvey7yUoA40W+aJFi9gbU5aqG3WByuMoJYFejyLL9eQlyD5n4ZkvulIEtPub7/sm+iK6faGHP7xfCwb1QmNFTvnaJAqqqZTnxAhN4PTp00xolHuT99hFZZKdmYrYyFDsnpPTt73dyOV4HBaF92nyR8efOG2A4SRLRKlpgqXGinz//v05M8/kyYJFHKxbt469Liq4UEYzpIJI3kXiksNhrFi6gOX8mJlbYKfNaTyLldP9ex+GNfNmwvaO+vZm1EiRUz9DmQ/r6iqulmm0EJWVzuXt4VIcqtk5TcNfBzdih90tqHOUUSNFTolOVFZGQldFYYSyIVdMloNOqb7yQJtLc+bMYddTglreTl7KItDFHgcd83QHy5Ygb29SdUEjRS4rjCjtiRGaAG0O0XqDNouuXLkiWIuGKo769+/P/i6U6diiRQvWSYCiNefPn2c9IRUXnsyAx8mtGG08E/aXXeHqcgVOx/dhj50LUtUw0UXjRE6V+JQ4RXkqimrDrK5cu3aNvdZWrVrh+fPngrVoqBpJFqEpOKh7AZXfUfcAKqimc4rob1ka3jy5inG9vsZXHTpDr2sXfN25E9q27oIdFwOFK9QLjRI5HTVIsxO9aXSaMvUYpAQnsQ7KIZGdUUQL0cKuyTvo+pYtW+YTd1FDtr9A2Zv0WMrepDYb8tSgZmWmIy0tAxJJJnMXaUgk6rvbrESRZyAk8B7c3G/DTzpr3Pe9h9u33FmH1zue3nj0PLLE51S2bt260DeMj7IPKvym6Aodzis2lCjydDzz98CelVPRsHYd1P+sK0x+WoPt23+BlcU8jBjQE30NJ+MP19ye3sUha8NMC06WRMRHvkFldY0bN/6HgPMO8tfp28HIyAirV69mj6PazvIIV6oKpbsrWVGX0V76x63TZTo+HiySlYnoh9cxWrcudGq3wT7XF8Id/xtZYYSiT4wQC/R3KShqOqWOFqQmJiasKsnDw6NcIi/qhNJFnvHqNnrX0kH9HnMQLthkhLn+jvrSN6LlqNWILybQStveNAsp68QITSciIgKdO3dGhw4dWMURpTrQHgItRrW914vSRZ4e445eJPLusxEq2GS8+/tPtP5EB5X1ZiI8z/tQWKhLVhhBzTS1guwP8L95AQd2/45fd/4OmxNO8H/xRvolmIzgx4+RUCCwRG0vqDi6LO0zxEr5iLym9Guz5zwUDFid3zKRCXfgYpt8pyZQgS9tasjyq+nrlUJg1B2WusqKnVBfZ0we0h0Gwydh46/7YO9wEgf//xdYLDDBd8OHYPCUlYjg7cnlplxEblDvE1Rv1Q+7HJ3x18ULcHI4BivzCWhcry4GfL8KwQn53zGKCdepU4e1OyaB29vbsw/DmDFjhCvEy/Pr+9GuViXoT1yPyOQC32jJUdg4UR8N9KfgJT9LRW7KReT9GlRA1cadYLZ6AzatXyudkWai11dNoVO5EcYv24ugN/nzLmi2lvUSNDAw+HjQ7JkzZ5g/Tic9uLm5iW4zKPWVN4xaVEXFFsPxIFkwFiTOG6azzOAVLu6NMEVSru5K3uKu1KRoWC8fy4Tcos8sBMblzuaypp15B4me4uRU/Eu7gNQtS2wdYi9vzTlc6/+sTgmWwsiAj4c7XkTynoryUq4Lz3/UjaQ+wncd/sXeWMsTfwtGqa9+/nw+gRcclKWXlpYmXC0SsmNgZtBE+voqYe2fxW/hc+SnXETOQoiFRFeAePw49DMmXNN9uW3TZE30CxsUJittzoVaE+8Fo9aVpa+xAfbdUUzvGE4OShc54j3Qq4bUXfnmn9GVpABHdKonFW+NTjgblBv7lh3+WnCoYw9BhfHmDga3qih9nY1wwEN1VftiRIkiz0LS2xh4O61DdRJpXT3sdr4MD08veLhfw+EdVuj5eQNUrNcOq/64k68Vmbm5+T8EToPOqxctmSGYrldf+jqrYP1Z+XaAOfKhRJGn4YGbM7ZYWWDuXBPMNTHB/AXm7MiRJYsXS4W8AKs278XdoBjh+lxk2/d5B53LI26yYW+Z08N8xDI7wVYEWRKkZfDoirwo310pBbLkf9no06cPO0Jc7CQFX4Y+uW9NesPlZRHlbFkJcP7jD/iGcZdGXtRO5FTjKCv9otGsWTNW1aIt+DqsQ4sq0jWM7kic83qB3DRtCRIjH8Hml9XY5XAT78UVPVUqaidy6m0oS/yn0i9q06BtPLx6FGO+6YTmzVqj96CRmDF3PhYtMscC86U49KfHx6Y+HPlQO5E/ffqUpYeSyOmIQK0l6x0CvN1xzuk0HE+dwaXrnohK4PIuDWonck9PTybwIUOGiG/Dh6MS1E7klIxF9Zti6YrFUT1qJ3I6XpC29TkcRaF2IudJ/xxFo3Yi53AUDRc5R/RwkXNEDxc5R/SoQOSZeOR5FUcOHsAhaxvY2Fjj0MGDrAUcjf379mDnzl245M0LBziKQQUiz0J8bARcjv6ET3V08ElDfWw4ZIMj1tawkY5d236Gwef10W3aLunHgcMpO6pzV1L9MLC+Dqp9NTG3s5ZA0t+nsMRqDwoU8XM4pUJ1In/nA8PGOqjx1Xg8+Uf3rDSEh0UgjYucowBUKPJ7GEoibz8BeTfwY54FIeSVdvXq4ygXlYu8ertv8SA5BR9SUvD+XRR2rbSEo2/BrokcTulRqbsyvGUV6NRshe9mzcU8U1OMH9YV1Wp3wKknfCbnKA6VzuSGTSugaitDnH8QgMCAANz3uQrzKdPh6B8tXFQ4qdJZn0deOPKicnelpu6kfP1YHrpdgefTwtyVbCSG38cWsymYarEb8YKVwykO1S88C0RXsjIzkZlVWLPyDEQ9uYuZvVqizeCl+VrOcTj/C9WJPNkHhk1yoivBJSjKdVxhDP3/LAHvMcWRF9WJPNMfgxrooFq78QgRTPJgZzlWKvKlXOQcuVGByLMQ9ewBnHaZo4YOtZ1ohBWHLiLwRYxcp8FxkXNKigpELkHoQy+csbfFcTt72J2wha3dGfgERch1PjsXOaekqM5dKSVc5JySonEid1hujO6jfgQ//40jLxol8vSUJPw6tQeadpmAJ4kpJT7RmaOdaJTIIwLcsOnHOZg2aynOuAXydmkcudA4d4XDKSlc5BzRw0XOET1c5BzRw0XOET1c5BzRw0XOETnAfwEUkzc0RR+LUgAAAABJRU5ErkJggg==)
' O ' is the centre of an equilateral triangle ABC
and
are three forces acting along the sides AB, BC and AC as shown in figure. What should be the magnitude of
, so that the total torque about ' O ' is zero ?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAALkAAACCCAYAAAAaEGkyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABTVSURBVHhe7Z0HWNNX98epe79q3b5qrdZW1KrgqIpbQX31rxbrrnWDIi6KVsW6V7W2/t0KalEQVIqrLlBEBUFALKiIA9ngYInICnzfnMsvMgovARKS/HI/z3MfzckvgZBvbs4995xzdcDhiBwuco7o4SLniB4uco7o4SLniB4uco7o4SLniB4uco7o0VqRB7kcw46j14RbHDGjpSJPxSbjNqjxxTi8SBNMHNGilSJPCXaGbjUd6OjUxZaLzwQrR6xoocgzYb9hJgYMMkLzyjpoZ7wB77KFuziiROtEnhHtjm8NjeEWFIQlA5tAp3JbnH6UKNzLESNaJ3LX30ww0nQXaPK+d9BU6rLoYNhyB3abI060S+QfnmLOKCMcuPMq53a8LwY3q4RKLYfC97Ukx8YRHVol8uBzG9Gj/xTcC4tFZGQkoqPDsOV7PelsXgmLj3kLV3HEhhaJ/D02TzNAx77fYumSRVhgZoaFiywwd5IRakhdlqb9zBHDJ3NRojUij/OzxeAh43E7JA4J8fGIi4tDXHwCEuNDsHhgc+ls/in2uEcLV3PEhJaIXIIjluMxa/M54XZ+Hjr9jNrS2Vx/+u/ge0PiQytEHnvPFh2btcEBn3jBkh9JyA3o16LNoabYc/0Zj7SIDNGLPMzvL8wfOxC6uvr4wWIjbjyMEe7JIe3VE1hvWoh+3Tuho+6XMBgxBUcu+nChiwjRi1ySmY7U9Ez2//TUD8jIzGL/l5GdJUFqatpHUUsy0j5ezxEHWrPw5GgvXOQc0cNFzhE9XOQc0cNFzhE9XOQc0aP1Ik9LS8PYsWPRo0cPXLx4UbByxITWi/zChQssp5xGs2bN8Pz5c+EejljQapFnZ2djwoQJTOA9e/Zk/xoYGCA5OVm4giMGtFrkT548QdWqVdG2bVtER0dj0qRJTOimpqbCFRwxoNUi//nnn5moly9fzm7HxMRAV1eX2fbu3ctsHM1Ha0WekJCANm3aoEqVKnj06JFgBe7du4datWox+40bNwQrR5PRWpGfOnWKzdjGxsbMN8/L8ePH2X2ff/45Xr58KVg5morWitzQ0JAJ2dnZWbDkx9LSkt0/dOhQfPjwQbAqAOkHKjMjQ7jBKQ+0UuR+fn6oUKECvvjiC6SmpgrW/GRIhWhkZMSEvnjxYsGqAD5E49LJQ7CYNxNTp07FLNMFWLZsGftQWVpawGTGBIwcMwPnAngpnqLQSpEvXbqUiXfbtm2CpXCoov/LL79k11pbWwvWspKNLEkqLm2ZzJ63g/Fq3Pf3Zx88Pz8fXDtnjSEd2mDhMU/hek5Z0TqRv3r1im361K5dG8+eFd8H8fbt26hevTpbjHp6Kk54sS7bUVEq8oFL7ARLLqFujrA+f5dXJykIrRP54cOH2Qw6ZcoUwVI8Bw8eZI9p3749oqKiBGvZCL+8FZWlz9l/4THBkgNbA0sykPIht1qJUza0SuTkZ/fq1YsJ9vr164JVPhYuXMgeN2bMGJbvUlZI5JWkzzdoqb1gId7B9YoLYpKEmxyFoFUiv3nzJhNq9+7dSyzU9+/fY+DAgezxq1atEqylh0ReTfpcehPXwV/qk/v7+8HVbgvGTrPEy3fCRRyFoFUinzVrFhPpnj17BEvJIB/+3//+N3uOkydPCtbSEX55G+v10ki3P0znzcc809kYoNsQTfvOwyteR61QtEbk4eHhbPHYoEEDtn1fWq5evYpq1arh008/ha+vr2AtOTKfvK+ZNdLT06UjDcnht7Bi1Va8iC/EG095BZc/7WB/9jreFB715BSB1oh8+/btbAaeP3++YCk9v/32G3uuLl264M2bN4K1ZMhEPmCRrWAh3uO+jx/eJuZvm5GaGIK9VvPx7X8M8VXLRug2bhXCPvDGjfKiFSInf7pr165sA8jbu+zdaykNYMaMGUzolKqblZVflPJQVHSlMML9r+PCrcfs/6HXd6BBhQb43SOC3eYUj1aI/NKlS0yQgwYNQmamYhzexMRE9O7dmz3vpk2bBGsu5L8fPXq0yNyXyKu/5Mzki/PO5IWTlZXHfUm4izF9jXDuKT8dQ160QuTjxo1jYrS1LV5QJYGyF5s2bYqKFSvi7NmzgjUHGxsb9jPNzMwES35CnVez+7vN3i9Y5CA9EU6/LYPVIVfBwJEH0Ys8KCgINWrUQPPmzVl6raKhBC8Sa6NGjfD4cY5LQYSGhqJy5cqsICNfglfqa9w4a4s5I/TYArZxOwOsO3ACgeHFzMxpb3Fh33K0qvEJWvWYgruhPM4oL6IX+fr165kIraysBIvi2bhxI/sZVAxNbowMWaaju7u7YJEiSUVsRAiCnz5nuTFhIc/w5GkIElKKyUyUpOF1TBT+vmGLr+tWQl/zY+BLT/kQtcipVvOzzz5juScBAQGCVfFIJJKPtaI//PCDYAX27dvHbGvWrBEsisFhzVh0HrYcCkwAFjWiFjlt2JDIRo0aJViUx+vXr9GpUyf283bs2MFsDx8+ZB8wfX19FgtXFI6bZmLOBifhFqc4RCtyCusNHz6cie7cucJPmCgNFBenErnCePDgAerVq8cWorRpRMgiMGX5JvE8sRnTzVbigusNuDhZw3LFFjyI5YUX8iJakVN+NlXiU2Hyu3eKW6Rt3ryZiXb06NEsF6YgDg4O7H7a/qeMxd27d7PbW7duFa4oOSFezvhxwRwsXrkBRxwuIOSt4r4VtAHRipyqeUhchcWwywLN1rNnz2YbS/T85Aq5uLgI9+awYsUKdt+IESNw9+5d9mGj5C7y3TnljyhFTv5xkyZNmD8cEhIiWBVLYGAgSxGgMCAJetiwYR9dFIIKpMlOSWGU3luzZk3W54VT/ohS5LLCiGnTpgkW5UGLSxI7tbCgnzl48GBcvnwZsbGxLKRI/jnFyuk+xZXQcUqC6EROLgEt9sidKOhGKJPg4GAsWbKEbTyRoEeOHImVK1eyMju6TYMWwgXbX3CUj+hEfuvWLSaobt26sUqg8oZyVqjyntwT+j1kMzwNcluK6g7AUR6iE/n06dOZoFTd5u3Fixes/Rx16aLaUPqdaCZPSUkRruCUF6ISOeWLUFFEw4YNWQPP0uLo6Mh6llNjoZ07d7JU3dJCcXUKJdJzkdAtLCyEe9SDrJQ38L1zE+537rKwq7fnHRYalQ136Tejl08g4j5obrmSqEQuK2YoKvNPHig9lp4j71iwYEGZw39hYWEfF6D0M9SFrJTX8L7hDJPhndn6oduw77F27RpYWa2G1aqfMG1sH9T7V1sc8IoUHqF5iEbktG3esWNHJiKKTZeWvn375hM4DcowJJGWFWogSmHNunXrwsvLS7CqB/cPm7DXOn5j/tM2JKmx2G46CVucHwgWzUM0IqejUOhNGjBggGApHbLWE3kHRWsUtWsq2wGlndiyuFSK5qGdBfu9Jm3+S7Dkkhz6EH7BfCZXOePHj2dv0okTJwRL6aAOW9SMn4qeKRxIM/v9+/eFexUDNfmn35X8fkUmbpWFgOM5rfMmbsor8jRER8VqfEqvKEROMWoK1VFa7du3bwVr2aBQIG30KEOESUlJ6NevHxOVMvPcS4JM5JO35e7a4u09bN1+GK81PKdXFCKnZj/0BlF3WE2BtvipdI5+77L2cFEEASd+ZL9L+wETpQvPtVhj9RNGf9MGXxuvgaYHPTVe5PHx8SxqQTM5zbyaBBVYU4lc/fr1Fe4SlZSA4zk+ea8Jy9kBBacc7LF10XcYOn0DkkrejECt0HiRy1JbKfVVE7fMZf1g9PT0EBcXJ1jLH5m78v2OvEfIvMQRG0e8KWSbIP3tM+y0nIG+vftgktla+EWobwNHjRc5JUTRm+PkpJmVMlTcQc346TVQCZ2qPqi5C8+8IcQM6TdlIjILrjzTX+Hw6rmYZr4Gh3dvxDdNK6Nxn9l4mqCeU75Gi9zHx4clYrVr106jt8upiwA1ISWRKTr/XV4KF3nhvA9/hLN/3YBsSR7jtgN1qjbBHvey7yUoA40W+aJFi9gbU5aqG3WByuMoJYFejyLL9eQlyD5n4ZkvulIEtPub7/sm+iK6faGHP7xfCwb1QmNFTvnaJAqqqZTnxAhN4PTp00xolHuT99hFZZKdmYrYyFDsnpPTt73dyOV4HBaF92nyR8efOG2A4SRLRKlpgqXGinz//v05M8/kyYJFHKxbt469Liq4UEYzpIJI3kXiksNhrFi6gOX8mJlbYKfNaTyLldP9ex+GNfNmwvaO+vZm1EiRUz9DmQ/r6iqulmm0EJWVzuXt4VIcqtk5TcNfBzdih90tqHOUUSNFTolOVFZGQldFYYSyIVdMloNOqb7yQJtLc+bMYddTglreTl7KItDFHgcd83QHy5Ygb29SdUEjRS4rjCjtiRGaAG0O0XqDNouuXLkiWIuGKo769+/P/i6U6diiRQvWSYCiNefPn2c9IRUXnsyAx8mtGG08E/aXXeHqcgVOx/dhj50LUtUw0UXjRE6V+JQ4RXkqimrDrK5cu3aNvdZWrVrh+fPngrVoqBpJFqEpOKh7AZXfUfcAKqimc4rob1ka3jy5inG9vsZXHTpDr2sXfN25E9q27oIdFwOFK9QLjRI5HTVIsxO9aXSaMvUYpAQnsQ7KIZGdUUQL0cKuyTvo+pYtW+YTd1FDtr9A2Zv0WMrepDYb8tSgZmWmIy0tAxJJJnMXaUgk6rvbrESRZyAk8B7c3G/DTzpr3Pe9h9u33FmH1zue3nj0PLLE51S2bt260DeMj7IPKvym6Aodzis2lCjydDzz98CelVPRsHYd1P+sK0x+WoPt23+BlcU8jBjQE30NJ+MP19ye3sUha8NMC06WRMRHvkFldY0bN/6HgPMO8tfp28HIyAirV69mj6PazvIIV6oKpbsrWVGX0V76x63TZTo+HiySlYnoh9cxWrcudGq3wT7XF8Id/xtZYYSiT4wQC/R3KShqOqWOFqQmJiasKsnDw6NcIi/qhNJFnvHqNnrX0kH9HnMQLthkhLn+jvrSN6LlqNWILybQStveNAsp68QITSciIgKdO3dGhw4dWMURpTrQHgItRrW914vSRZ4e445eJPLusxEq2GS8+/tPtP5EB5X1ZiI8z/tQWKhLVhhBzTS1guwP8L95AQd2/45fd/4OmxNO8H/xRvolmIzgx4+RUCCwRG0vqDi6LO0zxEr5iLym9Guz5zwUDFid3zKRCXfgYpt8pyZQgS9tasjyq+nrlUJg1B2WusqKnVBfZ0we0h0Gwydh46/7YO9wEgf//xdYLDDBd8OHYPCUlYjg7cnlplxEblDvE1Rv1Q+7HJ3x18ULcHI4BivzCWhcry4GfL8KwQn53zGKCdepU4e1OyaB29vbsw/DmDFjhCvEy/Pr+9GuViXoT1yPyOQC32jJUdg4UR8N9KfgJT9LRW7KReT9GlRA1cadYLZ6AzatXyudkWai11dNoVO5EcYv24ugN/nzLmi2lvUSNDAw+HjQ7JkzZ5g/Tic9uLm5iW4zKPWVN4xaVEXFFsPxIFkwFiTOG6azzOAVLu6NMEVSru5K3uKu1KRoWC8fy4Tcos8sBMblzuaypp15B4me4uRU/Eu7gNQtS2wdYi9vzTlc6/+sTgmWwsiAj4c7XkTynoryUq4Lz3/UjaQ+wncd/sXeWMsTfwtGqa9+/nw+gRcclKWXlpYmXC0SsmNgZtBE+voqYe2fxW/hc+SnXETOQoiFRFeAePw49DMmXNN9uW3TZE30CxsUJittzoVaE+8Fo9aVpa+xAfbdUUzvGE4OShc54j3Qq4bUXfnmn9GVpABHdKonFW+NTjgblBv7lh3+WnCoYw9BhfHmDga3qih9nY1wwEN1VftiRIkiz0LS2xh4O61DdRJpXT3sdr4MD08veLhfw+EdVuj5eQNUrNcOq/64k68Vmbm5+T8EToPOqxctmSGYrldf+jqrYP1Z+XaAOfKhRJGn4YGbM7ZYWWDuXBPMNTHB/AXm7MiRJYsXS4W8AKs278XdoBjh+lxk2/d5B53LI26yYW+Z08N8xDI7wVYEWRKkZfDoirwo310pBbLkf9no06cPO0Jc7CQFX4Y+uW9NesPlZRHlbFkJcP7jD/iGcZdGXtRO5FTjKCv9otGsWTNW1aIt+DqsQ4sq0jWM7kic83qB3DRtCRIjH8Hml9XY5XAT78UVPVUqaidy6m0oS/yn0i9q06BtPLx6FGO+6YTmzVqj96CRmDF3PhYtMscC86U49KfHx6Y+HPlQO5E/ffqUpYeSyOmIQK0l6x0CvN1xzuk0HE+dwaXrnohK4PIuDWonck9PTybwIUOGiG/Dh6MS1E7klIxF9Zti6YrFUT1qJ3I6XpC29TkcRaF2IudJ/xxFo3Yi53AUDRc5R/RwkXNEDxc5R/SoQOSZeOR5FUcOHsAhaxvY2Fjj0MGDrAUcjf379mDnzl245M0LBziKQQUiz0J8bARcjv6ET3V08ElDfWw4ZIMj1tawkY5d236Gwef10W3aLunHgcMpO6pzV1L9MLC+Dqp9NTG3s5ZA0t+nsMRqDwoU8XM4pUJ1In/nA8PGOqjx1Xg8+Uf3rDSEh0UgjYucowBUKPJ7GEoibz8BeTfwY54FIeSVdvXq4ygXlYu8ertv8SA5BR9SUvD+XRR2rbSEo2/BrokcTulRqbsyvGUV6NRshe9mzcU8U1OMH9YV1Wp3wKknfCbnKA6VzuSGTSugaitDnH8QgMCAANz3uQrzKdPh6B8tXFQ4qdJZn0deOPKicnelpu6kfP1YHrpdgefTwtyVbCSG38cWsymYarEb8YKVwykO1S88C0RXsjIzkZlVWLPyDEQ9uYuZvVqizeCl+VrOcTj/C9WJPNkHhk1yoivBJSjKdVxhDP3/LAHvMcWRF9WJPNMfgxrooFq78QgRTPJgZzlWKvKlXOQcuVGByLMQ9ewBnHaZo4YOtZ1ohBWHLiLwRYxcp8FxkXNKigpELkHoQy+csbfFcTt72J2wha3dGfgERch1PjsXOaekqM5dKSVc5JySonEid1hujO6jfgQ//40jLxol8vSUJPw6tQeadpmAJ4kpJT7RmaOdaJTIIwLcsOnHOZg2aynOuAXydmkcudA4d4XDKSlc5BzRw0XOET1c5BzRw0XOET1c5BzRw0XOETnAfwEUkzc0RR+LUgAAAABJRU5ErkJggg==)
physics-General
physics-
A wheel of radius 0.4 m can rotated freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung, An angular acceleration of 8 rad-
is produced in it due to the torque. Then moment inertia of the wheel is ![left parenthesis g equals 10 blank m s to the power of negative 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
A wheel of radius 0.4 m can rotated freely about its axis as shown in the figure. A string is wrapped over its rim and a mass of 4 kg is hung, An angular acceleration of 8 rad-
is produced in it due to the torque. Then moment inertia of the wheel is ![left parenthesis g equals 10 blank m s to the power of negative 2 end exponent right parenthesis](data:image/png;base64,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)
![](data:image/png;base64,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)
physics-General
physics-
A rigid uniform rod of mass M and length ' L ' is resting on a smooth horizontal table. Two marbles each of mass '
' and travelling with uniform speed ' V ' collide with two ends of the rod simultaneously and inelastically as shown. The marbles get struck to the rod after the collision and continue to move with the rod. If
and V=L mts/sec, then the time taken by the rod to rotate through
![](data:image/png;base64,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)
A rigid uniform rod of mass M and length ' L ' is resting on a smooth horizontal table. Two marbles each of mass '
' and travelling with uniform speed ' V ' collide with two ends of the rod simultaneously and inelastically as shown. The marbles get struck to the rod after the collision and continue to move with the rod. If
and V=L mts/sec, then the time taken by the rod to rotate through
![](data:image/png;base64,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)
physics-General
physics-
A circular disc is rotating about its natural axis with angular velocity of 10 rads-1. A second disc of same mass is joined to it coaxially. If the radius of disc is half of the radius of the first, then they together rotate with an angular velocity of
A circular disc is rotating about its natural axis with angular velocity of 10 rads-1. A second disc of same mass is joined to it coaxially. If the radius of disc is half of the radius of the first, then they together rotate with an angular velocity of
physics-General
physics-
Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The masses are held at rest at the same horizontal level and then released. The distance traversed by centre of mass in 2sec is
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)
Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The masses are held at rest at the same horizontal level and then released. The distance traversed by centre of mass in 2sec is
![](data:image/png;base64,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)
physics-General
physics-
Three particles of equal masses are placed at the corners of an equilateral triangle, as shown in fig. Now particle A starts with a velocity
towards line AB, particle B starts with a velocity
towards line BC and particle C starts with velocity
towards line CA. The displacement of C.M. of three particle A, B and C after time "t" will be (given if
)
![](data:image/png;base64,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)
Three particles of equal masses are placed at the corners of an equilateral triangle, as shown in fig. Now particle A starts with a velocity
towards line AB, particle B starts with a velocity
towards line BC and particle C starts with velocity
towards line CA. The displacement of C.M. of three particle A, B and C after time "t" will be (given if
)
![](data:image/png;base64,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)
physics-General
physics-
A mass
is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now, if the mass starts moving position of C.M. of mass of system will:
![](data:image/png;base64,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)
A mass
is rest on an inclined plane of mass M which is further resting on a smooth horizontal plane. Now, if the mass starts moving position of C.M. of mass of system will:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQcAAAB3CAYAAAAO/oXSAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABNrSURBVHhe7Z0JfA1X+8djLypBkVK1trHEVqWoWvovSluqSqm1jVJLLbFUdSVJk6pYqtSriqpQ1F55rbWFWmNpxC6JWkqJfc32++d3Mjci7nhDJsmduc/38zmfyMzkJnLPfDPnnOc8jwsEwYnp378/nnjiCezevVs7ItgQOQhOjchBH5GD4NSIHPQROQhOjchBH5GD4NSIHPQROQhOjchBH5GD4NSIHPQROQhOjchBH5GD4NSIHPQROQhOzaBBg1CkSBGEh4drR9LP8ePHERMTo31mXkQOglPj5eWFggULYvny5YiKikJERMQjtcjISNVmzpyJXLlyYciQITh27Nj/fE1e888//2g/jWMhchCcknXr1uGdd95RQ4rs2bOjTJkyqFSpEipUqPBIrWLFiqhWrRrc3Nzg4uKCHDlyoHLlyvD09LR7va0988wzqFOnDv7880/tJ3McRA6CU8G/1n369EG+fPmQP39+FC9eHHnz5sUrr7yCdu3a4e23336k1rFjR3h4eCgx2Nrjjz+uzrVt2/a+622tdevW6N69Ow4dOqT9hI6DyEFwCs6fP49x48ahaNGi6kmhVatW2L9/P7y9vdXTQ2hoKBISEh65nT59Wj05pJZDUFCQ+v72voYtPj5enXdERA6C5fntt9/w4osvqhu2bt266nMbAwcOVHLYt2+fduTR8PHxuUcMtvbcc8/h3Llz2lXmQuQgWJadO3eqx/Zs2bKpFYmxY8eqJ4iUGLGUGRYWpp5I7MmBbdiwYdqV5kLkIFiOEydO4JNPPlHDB84t9OzZU8012MMIOXTr1s2uFGzN1dUVW7du1a42DyIHwTJcu3YNkyZNQvny5dVN2aJFC6xfv147a5/0ymHp0qXIkyfPfUJI3Zo0aaJ+PjMhchAsAeMU6tWrp25ELiHOmTMHt27d0s7qkx45cIiSchKyXLlyePXVV9W/GzVqhPr16yNnzpzJ56dMmaJ9pTkQOQim5q+//kKXLl3UzcdgJk4Mpp5XeBDpkcOVK1fUnAbjFObPn68mHjl84M/CJ5jLly9j165dKgqzVq1aSlhmQuQgmJKTJ09ixIgRKFCggPrr3LVr10cKgTZiziElfB3KYfLkydoR8yJyEEwF9yxMnTpVRSTyJuRYfs2aNdrZh8doOezYsSP5ycHsiBwEU8CAoQ0bNuDll19WN1+pUqUwffp0XL16Vbvi0RA56CNyEBwexhH06tVL3XS8kYcPH27YZiWRgz4iB8FhuXjxIr7++muUKFFC3XCdOnVSN5+RiBz0ETkIDgeXIOfOnZs8r1C7dm0EBwcjNjZWu8I4RA76iBwEh2LLli1qUxRvsNKlS2P8+PG4fv26dtZ4RA76iByEZJh4JCAgANu3b9eOZB7MnsQbldunc+fOrWIDjh49qp3NOEQO+ogcBNy+fVutyz/11FPJj/Ec72cGDCnmhijmVeD3ZlDRtm3btLMZj8hBH5GDkxMSEoLmzZurDs3txbbwX64IcPkwo+D8wbJly1TkIL9flSpVMG/evAyZV3gQIgd9RA5OyqlTp/Dxxx+rTUNMSsJdjLaw42bNmqksSRs3blSfGw2HLUzRxpuIKxGjRo3KtCeV1Igc9BE5OBlxcXGYNWuWyl3ITtyyZcv7HuN5o3CfAvcMcP+AUZw5c0YlXi1cuLD63n379sXBgwe1s1mDyEEfkYMTsWfPHrz11luq83J+Ydq0aWq+wR6jR49W13311VfakUeHG5B+/PFHPP300+o1ma8xo55KHhaRgz4iByeAw4WRI0eqpCMcRvTr10+lTH8QDEtu2LAhHnvssXRlRl6xYoWSAW8Ybm9myDOfXhwFkYM+IgeLw3yJ1apVVx22Vcs3ELIp7X+xOTdAOTA3waVLl7SjaYPJW5mRmcuS3Dnp5+en5jkcDZGDPiIHi8KxfOfOnVVHLeyWDyOGD8IfyxdhT8Ql3Io+jqUzJmHitPnYf+5O4tUJiApdhf+MC8T0JVsQzUMavKn5Gpw0TAvMacCnFE5osnYDcy1QFI6KyEEfkYPF4PiecQNMeMqbs3uPnjgYuhGrxvdEcbeCqNvxc8yY5IOeHd5EVffcKNdiEIKCpuHTPt3Q9rU6KJS3CN4JWA1bDiW+HjMa8a//g24gzl2w2hOXJHlzcEjC7EyOjshBH5GDhWA+wwYNGqjOyZRpKW/Oq3/9hBfcC8Cz1efYHZU0RNgwvh1yuxRGR785iLgYB8RFYljjUiha3Qu7Uzw9cPKQiVq5XdreBObatWvRtGlT9X25CsJ0aBkZ8mwkIgd9RA4WwrbCwBv0vjmCC8vRpPSTaDZssXYAOLZ6JEq5lITfFtv25wTM7FEHxSu9ibWpvpxBUXztMWPGaEegwpuZ2ZnzCmyMlXDEeYUHIXLQR+RgIbjCwGhH/pXfvHmzdlTj7DK8kiiHpkPuFnQ5HPwVSruUhs/GSO1ILGb0eAHFPVtjbaqYJMY7vPDCC3jyySfVDskffvhB1YJgTQiWdWOuRDMictBH5GAxmHCVAUzcH3FPolW7cvgySQ4b7sph+gf25UC4jZodnysY/MghzOLFd59EzIjIQR+RgwXhhCQ76D0BTJdWolmZJ9F8+DLtAHBirS/KuJTBN9vuZlWa3bseSlR9GyE3tAOJML8C8zbaoird3d3V94iOjtauMC8ZJYeJEydqR8yLyMGCcHjB/RG5cuXCtsTOirgb2L/wYxRL7LQlXvbGjsgLuHTmGIK+TNpw1TJgASL/uYhzR7fgw9oF4ZK7PL79Iwqck9y29U+88cYb6jq+HucYuLXbKhgtB4ai83c1YcIE7Yh5ETlYFNaJdHNzQ/2XGuDquUiELJwCP19f+Af+gFX7TuLskV2Y9+No+Pr5IvCnhdh37Awidy3HpMAABI4eB7//LIFX38Eo6FpAdXbOZTDa0WoYLQdOyPbu3TtLcmIYjcjBwtgCmHy/9teOpI2VK1egzvNJUZXM8sx9EenN8uyoGC0HKyFysDA3btxQpee5pyItf8lCQ0OTt1JzxWPAgAE4e/asdtaaiBz0ETlYHOZkZL4Gbn6iLOzBVQ3fxCFHoUKFlBi4jdtRdk1mNCIHfUQOTgDLxvGm5wpDahYtWoTq1ZOGEM8++yxmz56NO3dShEdaHJGDPiIHJ4BLjkzcws1Qtk1Qhw8fVvUlKQUeHzZsmCWWJh8WkYM+IgcnYdOmTWrYwP0R/v7+KtKRYmAaeCvMrD8qRsvh1pXLuJG5aTAzDJGDk8C9FrZkrmyVKlVSCV0dKfFKVmCMHGJxck8w/Pp2QMv2QxFikQcwkYPF4STknDlz4OHhoVYg+NHHxwf//vuvdoVzY4gcYmNwOnwpOlYvhOxFXsHyc9pxkyNysDBcceDKA58UGPrMeH+9FQtnxbhhxR3M7FUfRcu8imCRg+CoHDlyRFWlZvUobpLiZGNERIR2VkiJcXKIRVDfl1CsbKIcLmiHTI7IwUIwaxPzLbCz82mhTZs2KrBJ0Mc4OcRgVp+XUNzjDaw4fQl7lv2I4UM/x7QVe3EzXrvEZIgcLACrRDFe4fnnn1dS4McFCxZoZ4UHYaQcZvdrDPeSNTFodCA+7e+FVvWfRR7Xqhi1IgJm9IPIweQwbXzKWhQMdHrYTNHOjKFy6N8Qrm4VMPL3A1BrQKf+i/9zdUG9Ib/CuNJAmYfIwaScPHkS3t7eat8ExcBOnhlVqa2G0cOKYuVfw+rL2qGLB9CrajZU7j4VZlwbEjmYDNaUZEVs1pikFLiV+r6UcEKaMVwOZV+9u5R5YT96V8uByl4iByGDYXZppnynFGrWrImgoCCnD2JKLxkth14iByEjCQsLU1upmYmJ9SO++eYbVZRWSD/GyQGY278h3Mu1uDusuHoUH9XIDs8eM2A7ZCZEDg4M5xW++OILFavAGpfvv/9+llelthrGyCEW0VHb0K9+kcSnutLw+e9RXLx0Hsc2z0bDfC7IWasX/jh8LvEqcyFycEBYOOann35C5cqV1RCCuRismKLNETBEDgm3cWzLb/AdPgiDvIci8OfViIo6gnWLp+BT78Hw/sQf89aFJ1cRMwsiBwdjzZo1aNy4sZIC8yuwKrVZqkeZESOHFVZD5OAgHDp0CF5eXkoKzNz02WefWT5FmyOQEXJgshwWFDb7ZLHIIYthJ2J+BVaPohg6dOggIc+ZSEbIgRXBmFznwIED2hFzInLIIuLj4/HLL78kp2jjEuXvv/+unRUyi4yQA2tW8D01ex5OkUMWwJBnBi+xAzEjE7dSc9OUkPlkhBxYR5TvrdmD00QOmQjnFZjunR2HBWf47xMnTmhn00M8zh7eiZXBy7Bs+QqE7D7+4Jnx+EsI2/oHghOfVIJXrsH+vy8jQTvlbIgc9BE5ZAIsCMPy+GXLllWdpl27diplvHHE4/T+EEz+uC2KUjwV3sSSCP1V9QshE1CrSF64FKqCQd8twe6IaJGDyOE+RA4ZCGetuZW6Ro0aqrNwfoGfZ1jq97AgNC7JHJF50NZ/tU7QzXlM/SgpBDt/jU7YbMbtggYictBH5JBBsFZl+/btVSfhVuqAgABcuZKxd2LCvl/RqUNzVCuQHa7VOmHjmfv1cGXnHHTt2BDl3QqiRO2uCHHy3d0iB31EDgYTFRWFIUOGqK3UOXPmRN++fdVcQ2ZwJ3QmegwYgQlDXkMuF1d8MHV7Ul4BGwlX8euIXhgw2g9dapXEE9U6YtNF7ZyTInLQR+RgELdu3VKrDiVLllQdo0WLFggJCdHOZg53dk6H16DR2LltOVqXcsFjdQcgPEX92+vHl6Nn+w8RfGQHvGsWglsVkYPIQR+RQzpJSEhQ+x4aNGigOkTFihUxc+bMLCkpd2fnNHT+6Bv8feUyFg9nCPYTGLzkuHY2Aeu/+xCdPluGOziIDyu7ihwSETnoI3JIB4xk7Natm+oIxYoVUzUpWZQ2q6AcOvXywZFbwNW9M1CzgAvcm4zASZ68sh0D2rbHjH1c5NyL7pVEDkTkoI/I4RFgQRhupbaFPHfv3j25BmVWkiSHEdjP1Ojx5zGuQyW4ZCuNwO3RiFj4Cdr2m4KkYkyhIgcNkYM+IoeH4Nq1ayrkmQVi+ObXr18fq1evVqHQjkCyHP5Nilo4t8YXJXNkR6233sf73Xpg8jpbwNUukYOGyEEfkUMaoQQ4ycg3nXkWpkyZ4nCl6mNDZ6BzHx8csBVViYvCiOZPq5+5UpfvcCo5bHI3PuCcQ1WJcxA56CNy+B+wVD2HDczGxMat1FyudDTiYm7jVLA/GjTthvUR1xETl/Q0c3BuL7jlLYFPFyYtp8bHxeDm6WVoUcwFLu5NsPDwTdyJNWnVFQMQOegjctCBE4ujRo1SeyBy5MihQp737t2rnXU0YnFs6yL49G2L2s83QJ+An7H1UFKW05hT2zEhYCx2qKeJeJw9uAmTv+iJhjU84Vm9IXp+PgHrwv+R8GmRw32IHFLB6lEsTc/sznyDuS9/8eLF2lnHJT4+FrF8WkhIUP+H+Hj7t3tCfBxiYu6GRsXFxiBO51pnQOSgj8ghBQxaslWlZjDT999/L9WjLI7IQR+RQyKcQ2AnYYZnhjyzkpQxW6kFR0fkoI9TyyE6OhoTJ05Mrh71+uuvq0QsgvMgctDHaeWwcOFC1K1bV72JtWrVwvz58x0mXkHIPEQO+jidHLji0KZNGzV8KFiwIAIDA1WSV8E5ETno4zRyiIyMVDEKuXPnRr58+dCjRw+pSi0YIgdGzqaEhY4ph9TZvhgz42iBcw/C8nK4efOmimasUKGCesMY5cjCMYJA0isH1izlk+h7772nqpRduHBBfWRfY8Kf06dPY9asWaomSfny5bFgwQLtKx0fy8qB8werVq1CvXr11Bvl4eGB2bNn48aNG9oVgmCMHPLnz6/6GBtTAjK8Plu2bGrvjaenJ7Jnz558/ueff9a+0vGxpBzCw8OVyflmFC5cGF9++aXaSSkIqTFiWMEVL9vN/6A2cOBAxMTEaF/l+FhKDiwfx5wKfLP5ZjDXguOGPAuOgBFyYG7QRo0a3SeDlK1KlSqmm/i2hBxYk5CPa8zCxDeChWhXrlypnRUEfYyQA1m6dOk9w4uUjUMMLpWbDdPLYdOmTWjWrJl6ExjyzMlHqUotpBWj5MA5LtY5TS0GtnfffddUwwkbppUDi5T27t1b/fK5c3Lo0KH4+++/tbOCkDaMkgPZs2dP8pDW1tzd3REWFqZdYS5MJweO71g9yjaEYLyCI6RoE8zJ4MGDVbq/gwcPakfSh6+vb/LqBGNqWFTXrKRJDowVYAAHf4FZ1Vj7geM2bqHmL55PC8y3QCtzLTmrfz5p5mvsU126dFF9iZXI+Lm969La2AeZMax48eKqj3L5fNeuXfe8LuMgzEKa5MD/MP+z0qRJS19j8WSzkCY5cCw/ZswY+Pv7Z2ljSTk+LdgaP7d3nTRpaWljx45VT6K5cuVScw/ffvut3esepqXuo6nPrV+/XrurHB/TTkgKghEwxJl/+IT7ETkIgmAXkYMgCHYROQiCYBeRgyAIdhE5CIJgF5GDIAh2ETkIgmAXkYMgCHYROQiCYBeRgyAIdhE5CIJgF5GDIAh2ETkIgmAXkYMgCHYROQiCYBeRgyAIdhE5CIJgF5GDIAh2ETkIgmAH4P8BIfhyI5jYRjkAAAAASUVORK5CYII=)
physics-General
physics-
In a sphere of mass M and radius R, a part of radius R/2 is removed from it according to fig. Centre of mass shifts (x) towards negative x direction, then the value of x in terms of R is :
![](data:image/png;base64,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)
In a sphere of mass M and radius R, a part of radius R/2 is removed from it according to fig. Centre of mass shifts (x) towards negative x direction, then the value of x in terms of R is :
![](data:image/png;base64,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)
physics-General
physics-
A wire of uniform cross-section is bent in the shape shown in fig. The co-ordinates of the centre of mass of each side are shown in fig. The co-ordinates of the centre of mass of the system are
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)
A wire of uniform cross-section is bent in the shape shown in fig. The co-ordinates of the centre of mass of each side are shown in fig. The co-ordinates of the centre of mass of the system are
![](data:image/png;base64,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)
physics-General
physics-
The figure shows a metallic plate of uniform thickness and density. The value of l in terms of L so that the centre of mass of the system lies at the interface of the triangular and rectangular portion is:
![](data:image/png;base64,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)
The figure shows a metallic plate of uniform thickness and density. The value of l in terms of L so that the centre of mass of the system lies at the interface of the triangular and rectangular portion is:
![](data:image/png;base64,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)
physics-General