Physics-
General
Easy
Question
A uniform thin rod is bent in the form of closed loop ABCDEFA as shown in the figure.
The ratio of moment of inertia of the loop about x-axis to that about y-axis is
![](data:image/png;base64,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)
- > 1
- < 1
- = 1
- = 1/2
The correct answer is: < 1
Related Questions to study
physics-
In the figure shown, a small solid spherical ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is
![](data:image/png;base64,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)
In the figure shown, a small solid spherical ball of mass 'm' can move without sliding in a fixed semicircular track of radius R in vertical plane. It is released from the top. The resultant force on the ball at the lowest point of the track is
![](data:image/png;base64,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)
physics-General
physics-
A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown in the figure. About which point will the angular momentum of ball be conserved.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANUAAACKCAYAAAA9mA+hAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACvlSURBVHhe7Z0FmFZV1/ff6/2e73lsHzsRRQREOgXp7u5upEO6wQAkJIYSBKRLwiJEWiWUECkJCSkJQSVEYb37t+5zZs4cZgaQe2buYfafi2vm3veZE/vs/9prrb3W2v8jFhYWQYUllYVFkGFJZWERZFhSWVgEGZZUFhZBhiWVhUWQYUllYRFkWFJZWAQZllQWFkGGJZWFRZBhSWVhEWRYUllYBBmWVBYWQYYllYVFkGFJZWERZFhSWVgEGZZUFhZBhiWVhUWQYUllYRFkWFKFOC5evCiXL192PlkkBFhShTjWrV0jfXp0l0uXLjotIteuXXN+swhFWFKFMP78809p0qCePHz/3TJvziynVeTwoYPSsX0b2b1rl9Mi+vuwIYPtrBYCsKQKYUyfOkUeeeBe+e+9/5EcWTLKkcOHtf3cuV+lYN5cMmLYe/oZvN2vr3R6o71cvXrVabGIL1hShSj279snBQxxMqVNLXlyZpd0qVNKu9Ytw1W/Ee8NlQplSsnff/8tp0+flhJFCsnKFV/qdxbxC0uqEAREadqwvtSqXkXe6ttbqleuIJMmjpdkzz0tn368SI/ZtWOH5H3tVdm3d69RDWdL2ZLF5Lffzut3FvELS6oQxOSJH0i6l1PIrl07JWzEMClXqriqfI3q1TXtKeXgTz/pca2aNzVqXx+pXb2aDBs6WNss4h+WVCGIGdOmypTJE/X3we8OkJJFC6mt9P22bdK+TetwUi1auECypE8r+XPnkG1bt2ibRfzDkioE4XWZvzvgHSXV77//7rREgLbsmTJIzaqVrYMihGBJFeJwSfXbb785LZFRt1YNGT9urPPJIhRgSRXiiIpUzGSXLl+SmTOmSaH8ecJd7RahAUuqEEdUpGKBt//bb0rWDOnU/rIILVhShTiim6n27N4t27/f5rRYhBJChlQMlM3ffSc7d/zgtIicP39eVq1YIWfOnHFaEh9uZFNZhB5ChlRXr/4tDevVke5dOjstYiTx95ItU3r5+qt1TkvigyVVwkNIkapqpfLSrnUrp0Vk65YtkjJZUlmzeqXTkvhgSZXwEFKkqlmtsnRo19ZpEdm2daukSZlc1q5Z7bQkPlhSJTzECam8i5kurly5Ij/t3y+nfvlFP0Oq6lUqaqS1C9Q/SypLqoSGWCfV77//Jr26d5WwYcOUSC5279yphOnbq2c46WrXrCZtW7XU3wFhOalefN6SypIqQSHWSXX2zBkpW7K43Pef/yetmzeTY0ePavuZM6ckX64ckjl9mvDZavz7Y+XVLBk1j+iTRQuledPGkjldGmtTWVIlKMSJ+nfyxAlp37qlPHTvXVIwTy75el3Amzd+3Bh54K7/L59+8rF+vnDhgqY6ZE6fVooXLiCjw0bIxAnjI2W4JjZYUiU8xKmjgpSG5EmfleefeVJmTp8mu4wK+GrmjBq/5sXZs2c11cHCkiohIk5JBUhRKFmkkDz20P3SpeMbUql8Wc0dctMZLCLDkirhIc5Idd7MPKR9k9V6+NAhadmsqTzz+CPy0vNJJMmTj8n4sTbSOipYUiU8xBmp2rdpJY89eJ8m1ZUvXVKqViwvKZIllUdN2/3GriJ1nOpBFpFhSZXwEGekWrhgvs5OjerXlSoVymmhkvy5c6r3DxvrhWefkuVLlzpHW7iwpEp4iJZU58+dU8fCsiWLZcyokfLOm/1kw/pvNNuUVO+3+vWR98eOljNGpbsVsFb12/nz6hE8dPCgeva2btks69aslqM//+wcZeHCkirhIVpSYffkyJpJKpcvK4MG9FeXeO4c2aV1i9elR9fO0rtHN8mSIa0Szo+jR47IuDGjZMSwobJi+fIoIyosbg6WVAkPMZIK0owbPcppESlXqoRW9nHx9pt9pUaVSlrv2wULubWqVZEH7/mPPHzf3fLsE4/K1A8nO99a3CosqYIHnGS/nDwZ60I+RlJlzZhOFsyf67SI1K1ZXZo2auh8EjNLheki7cmTJ5wWkc8//USee+pxefqxhyXp009oJIV/Hcri5mFJFTx8ufwLaVSvtpw5c2smy63ihqTy1vCuXb2qNG5Qz/kkEjZiuL7wX3456bSIfPLxInn2ycfCSfXgPf+WWubvLP4ZLKluHyeM/f7l8mWyf99e3fDBG4MaGwg6qU6fPiX1zMz04N3/1jrgTz7yX0mfOpXaV39esS7zW4Ul1e1h44b1UrJYYalYtrSc+zVuonSiJRWeuVdSJpdZM6Y5LaJOizo1qjmfRN4bMlgK5HktkvoHTp86JWPCwmTIoAEqGWbNnCGZ0r0i9WrXMOe1kRO3gkED+0spMyiiqvtnET2w8wk2GBU2Qpo1bSQH43DcRUsqDLpWzV+XNWtWOS1GavZ/R7drcfHxwgXSo1uXm5IAhCdR7/u17Fll6ZLFTqvFjTB08LtKKlss8+ZAP+344QepVK6MdO/SSff1iuu+i5ZUsYFz585JT0PC1C+9KAP7vy0XL1xwvrGICgcO7FdBRN7ZB+PHyeXLl5xvAkAak0qDVuH+/+mnA3IlEUemXL16TerXrqk7opA5Hh+IU1K5mD9vrqqDuOMptWVxPc6fPyeVypfRdBns0kfuv0dGDR/mfBsA3izsrVJFC2voF/+L5M8rbVo2VxU8sQAX+fbt35vnbiE/mJ+7du7Q/osvxAupAA9etWI5rQW+cP5HTquFixWGMGyd43pRH7j731KjckVda3FBMmeGNKlk3bo1OkPxf/03X+sWO9hidzL27N5lCLRd/rpyRQ4dOqTJrfSTu9VQfCLeSAUu/PGHvNW3j6R8Man0691Tw5csAmADt2RJntZZKrDe9y+d2b32wawZ0yV3jmzXrbt06tA+kpf2TgKz0oRx4yRtqpc0w6HTG+1k7do10q1TR1n+xTLnqPhFvJLKxWeffqKSBj2YuhQWAXuJcDBmqqcefUjSmEHkl8KzZ87QULIN69fL8WPH5MTx4xpDWaFsaVkwf55z1J2FBfPmaXDB4w89IE+bfrn33/8r3U0/hRJCglRg3759UrNqFcmYJrVKYItAzfQWrzeRbBnTyXffbnJaI7Dgo3laF5FI/1zZs0quV7NKyheeU8+XW/fjTgMazUP33aXEIrsBUlGENZQQMqQCDCJsgdQvJdNSZYm53LMLXOqlixcxfXO9R2/u7FlKqLFjRslHc+eoAwiBxHamLZo2kb/++ss58s7A2bNnpHH9uvLfe++SJx5+UJ4wsxUxpgPeecs5IjQQUqRysfyLpZIza2b1bG3auNFpTZyIKaIiOpuKVJqc2TKbvtvgtCR8XDO2JGuiqMLVjNAoWjC/bjDerXOnkPN0hiSpwOHDhzXciRCnSRPGa6cmRtyQVGZg/epbfP9w0geSKvkLsnLFcqclYYP1JtbjPpz4gYwdPUr++OMPLQ7klmfw4uTJk1p7/8NJE2X1yhVy6VLktb24QMiSCvz11xUJGz5MXjYDpHWLZnL8+DHnm8SDmEhFRaqXXkgiPbt1lZGmn/jfuUN73Wwbr1h8DKhgAnOARe8Uxk6cOOF9pzV6fLVurRTMm1vX6koXKyJ5X8uhavCxY4Fak3GFkCaVizWrV6maU75MSU2KJDh31MjhGnV8pyMmUu3asUMGGxu0e+eORg0y/zt10IiVjxcujPVI7NgG9092OGuZZJnfyPGy44ftUjh/Hq3QtX/fPrW/ftyzW2pUrayOG5Zv4goJglTg+PHjuoHBow/cK8889rAaqcUKFbjjS5sltih1ZtfZM2eqc4bllZvJfbr852WpU6O6sbPyXRfnt8cQCy3nyOFDTkvsI6RJhRt5y+bNzieRZk0aycP336MlzShvRiWmRQsXON/emUhspKJ68ROPPKhqHBtU3Az2798nr2XLIiONBhMd4rKkQ8iSiik8Z9ZMkjVDWg1pwj1MWTNS9FmjIE3/4fvvvuPDcRILqX7cs8eo+av15/D3hqhmcrPgb/LmyC4LQiTcLWRJNXLYe1ojI1f2LDLQWYfAm5M53SuaAIk0y5ohjWR45WUZMmig/GmM2jsRiYFU67/5RnK/mlVtH7x6twpIlceQinW7qEB0Ck6vuEJIkgqXKRHX5G9BKCLaf3EM1fVff6VGOUTat/dHmTV9uqRPnVKLzRzYv1+PuZNwJ5MKl/ivv57VTSga16sje3/c43xzazh16hcpnD+vdOnwhtMSAQq0dunQXr5YFnc1JUOSVMuXLZPsmTPI8WPHdWNt1lxwH0cHFjtZDMyRJaN85uwgcqfgTiXVVmMrU1CVepK4zm+3OnHXTh102yWSa71gLS9NiuSaVh9XCDlSYVB2at9O2rVu4bSItG3VQkoXL3rdQp8X5M+wNkMs3Jt9ekcqm5aQcSeSioV8yjKUKVFUyRUMHDv6s9SvXUP3jZ42ZbIWgq1WsYIkS/KM9OrRzTkqbhBypDpx4rhkTPOyFC9UQEnSqX1bKWZmoeRJk4TvaxUTiNxOZ9TBqhXKac5NQsedRCrUvRnTpsruXTtlh9FAyAQPJnDHjxo5QiNxGtSppYWKsM0xJ+ISIUeqaVM+lHyvvaor6OPHjdX/kydO0H2s3mjb2jkqZrAQWK5kccmUNrVGcidk3CmkOnLksJQvVUKee/oJ+TJE8p5iCyFFqqvXrkqFsqWkX59eTksEcFqgM+/98UenJWaw13DP7l3lxaTPal7S7wl0UCZ0UlFXg3WkQ4cO6uYUOAzu9N1dQopUpIK/mjmDrlf4QQ0CsmBHmOn8VvDRvDmSJX0aMzALa/p1QkNCJhWJk21aNNMKWj8dOOC03vkIKVLhIl+2dIl6g/wgFowM4U0bbj2dgZ1FqFmYJlUKo9NH70UMRSRkUrF9Eik8c2bNTPDBvbeCkLOpYgsXLvwhfXv3VO8gttk/WWSMDyQ0UlH0kx1hBr7ztuY5/ZwIt0dKNKRyQZ0HQp+KFMgr3337rdMaukhopGJhnk0pOrRvk2jrOiY6UgFSRmpWrSxpUryo+TqhjIRCKhbg2bSP5EC2X0pM6p4fiZJUgMVhgnGTJ31WWr7eRHeGCEWEOqnwqhJKluKFpDJmdJjTmriRaEnlAscI9Rzy5cohX61d47SGDkKZVNTQ/37rVk0O7NW9my3U4yDRkwqQ6MhmYC8lTaLbA8V2FaKLFy/o7pIY8xTNjAmhSCq8s2w/S9AzG08cPWr3avbCksoBC5Ij3huq3sGGdWtr4ZnYAPGL3bt01rJaJGHWq11T3hs8yPn2eoQiqbBD77/rX1ri4Ptt8bMJQCjDksoHZo58r+XQsKjYKCNMpnLm9Gm1fgIIGzEsUGYsml3+Q4lUOHhQkb/5+it5561+cZqinpBgSRUF8GK93rihOjEGv9s/qJ6sju3bqufRBXGKr2XPIsui2bMrVEj18aIFmtdWskgh+f03uwFdTLCkigbYVe+PHa3l0apVrih7995czOGNQNgONePXrlktGzdukLmzZ+o2sNHtfBLfpCKlhrqCXTt31HIGu3bujPNN1BIaLKluAFSdgnlyaWr/px/ffgJk+9YtJX+unDJ2dJhMMLbJW3176wzATBAV4otUbBy3etVKKWCevU+vHnLp8mXdtsbixrCkugmcPHHSkKGVJHv2Kenbq+dtRLxf043JcIS4wE7Bpf/JxwudlsiIL1KRQUsKTvHCBTXQ2eLmYUl1k0DlIVrg5ZeSScVypeUHYwv9E5CRSiS+u/k4SXts0sbWolEhrklFQh+bye3evUujJO7U3UNiE5ZUt4hvN22SEmaQp3s5RbTVe2IChU7ISO3VvasSpXXz12X0qJHOt9cjLkl14MABKVuyuEZHfLxwvtNqcauwpPoHIC2cmuXscMia09lbjCSg6lOPLp10oXnunNkxlmh+b8ggKVGkYKySiusfPnRIVq1cIdUqVZBP77DiOXENS6rbwKwZ0yStmbFwM2/+7tYi3v/4/XfZ56kFf+HCBd2tgkgLtozROgt1a0n2LBmlSoWysUYq9gluVL+O1KhSUVW/hF6DPRRgSXWboN53mRLF1PU+ZfKkW3Y3b1z/jXoAKVucNlUKyZcrp5QpXlRJVbtGNd2WtEqFcrFCKipXDX53oFYC/mLpEqfV4nZhSRUEnD93Tnr16CovPPuUtGvdUr2FNwKLvtRsoEQAm5f16NpF1S5mL28eUmzYVBQm7W7Uz5lmpmU/p0MH7+xNHuIallRBxMIFH2l5NNa1UOWiwr69e6Vbl466cXj5MqVk0YL5Me6fRHpKMElFZi618R669y4JG35r9T4sbg6WVEEGNe2oh5Hqxed1gfeKp4b3ls3fqdcQVXHC+2OjrMXhRzBnKnbROHbsmO4j/P7YMdZ+iiVYUsUCMPj7v9VPvYNs/0MsIRHpRFKwg/yt7MUbDFKd/fWsRsKnMzbb6pUrnVaL2IIlVSxi8WefSraM6dUJwQxVt2Z1OXWLmz7fLqlINcF+w24bNnRwUG0zi6hhSRXLoJBkrepV5MG7/yP9337Tab15/FNSYTtNnjRBiXzgwH45fcpGRsQVLKniANhOw4cOkZeeT6Ku8gOGaDeLf0qq6VM+1A3yKpQpHb4NkUXcwJIqDrHiy+VaXDJrhnSy+NNPndaYcaukYmZkS1ecIgP7vx1t8qNF7MGSKo5x5PBhaVC3tryQ5Cl5+82+N9w1/VZIhQ2XI0sm6dCujfXsxSMsqeIBJECGjRyumcVESxARHh1uhlSEOP12/rz06dlD00rYDMAi/mBJFY/4et1ayf1qNsmYJrV8NG+u0xoZMZEKzx6LzATcYkMxOyXmIpahAkuqeMaJ48d1Lev5p5+Qnt266IzjRUykQpUkNwsHyBdL425PW4uYYUkVAiCwlQiLZM89I2VLFJft329zvhEZ/O4AKVWssKp4LvidHVBI1yCq/Z/shGIRe7CkCiFs2PCNFMibS15JmVxmz5qhZMODx87r7lae+/ftkxpVK0m2TOnlh+3fa5vFPwcBzGy+HpNj5/jxY/K5EWJewUaEzDfRlBmwpAoxnD59Stq2bC4vJ0+mqR+Z070iSZ56XOrUrC579+yRbzdu0NhC3PN//x27lXQTAz5euECefuxhLWrq1mL0g4DnsiWLqXoOtmzZLEUL5Vdva1SwpApRkG7/8H33yFOPPiRJnnxM7v/Pv6RsqeLGtopsc1ncHpih2M2e4qlpU70kkz6YIJcuXXS+jcDHixZK6peSycQJ45WAlOxGk4gKsUaq/Xv3ys4dO+TgwYO6NSX1yjGsaWNnQz7TTsETft+2dWt4m7YfOqg1E/zteo4fthupsidS+89HjmgUNvX5/O2UJkZtctuxRUjB2PHDD+HH8Z9z79m929xj5HbOwT3v4Hmcc/CTeyeujn2I3Xb3edgK1XtN2n8yv2MvueflP/fCs+w09+Ieyw79VIBFgkIoAnMfuf8eKWakI/fBPXqvyU/Oz3OSqh9+Te3D/aom0u5ek43YuJ73PWi7eU6e3dvOT+6R3eS5bsS5D+nzcU3vOTiWClHbt20LPLOnnT7nHYW3/2TaTZ/TJ96+4ifvgs0PvM/DT87DmPA+D8fuNve2a+cOPafbzvPQ5n8erk/hHu6H87FAvmrFCq3H+NiD9xsNoapWkMK76gWbMJD/1rVThxjr7ccKqRjYBHBiYKOqVCpXWgsxFi2YXzdcq1CmpGkro/+piUCJrtw5suuaDZWKKpUvo8cjPciEJZ2cdo5l7152nac4Pn+v7ZUrSvHCBbR+XsS5S0t1087mbtTsq1jWnNe0Vzbn4n+2jOmkUN7c4efmZ2VzXdStogXzhd+L/jR/myntK1qui+M4D/dH3lT2zBmc60U8D8+eI2sm/Vvug3buJVf2LBpc656bvkGtyPDKy/pcfHafk2h2iETe00P33S3/NT+pZFs4Xx5zfKrw59e+qlTeHJ9N3fM8A+2ci+vkyJJR8ufOqZ/d90BxF/qwdPGinvZyeg/sj1zOzIiB9sBzFimQT/uLQedek3vk2akEFfE8ZfR3ji2ofRvxnPwd74ExEOjDwPvBXqRdz6v/A+30LcHIEe30YQUtyU3fcg8cyzXYfN19P1yLa3Lf5UuXkIzmOSPGYeB5yBbQc3jOTcJoZXMuBNn//s//SHkzjiCfF5998om+h/ZtWjktUSNWSIXu2bhBXZWSpD0gMX4yv1c1N81Oez//fETbjhtddcnizyWPeTHop0ho6nPzc96c2bq9zepVK3RDZqTRCWMwNmlQT5o3aWwe+Cc9D+38r1G1snTq0M5InoN67p+PHFaJicrU/81++pn2U7+clBnTp0g+M9DWrV0dfk1smTFhI/WlY4SGt5/6Rd4xf88L+sFIVO7lqLnunt27pHSxIjJoQH91ix8x52f3C2pVMKAolEntPM5xzLSvW7tGB8ScWTNM+wltR0KiRjRpWN9I053aV7QfP35UvYHNmzSSRvWoH1FJOr3RTjas/0be7Ntb+vXuGf6c3M+a1at0cNNn9Cn3cvLECbUX8hqCkyqvfei0tzE2W32jwuz9cY/eG31z9OgRbaOCLtJc35t5TuIUK5pBx5aj7rukbxbOn2cGZw617U46fcVzTTbqU6F8uVXSY+DTfsr0IZs/MOi3bdmiNoq+H3NuhCDlBOg77o/zM1sWM0Jy+HtDwtu5T1JmCuR5TaZM+kA/0872PYMGvCOljEBg1gyMlcA1yW5GWOzeuVOvybk4pqgREqPCRuh44hk5dpfp/xavN5Hnnnxc6taqodfyqneMsQqlS2kuWrlSJTQfLToEnVRU5GHWgFBeTJ08SSWq68VyAUHwcHnBhmx1alSXcWNGOy0BMEWXMgP5oJnivSDjFslN53gxcfz7UrNaZT2fC36nlvkH5jsvqIiEJPaXX2aAsU60ZtUqpyUASkLjPPCeG5BHxSZyV69FrlVB9aVunTo6nwJg4/DGRkKigvjBgETF2/zdd/rTBYPOjzfatJbeRjXxAvWEgi7+HUU2rl8vJYoUUlXOi6VGuFFr47gREF7MnDZVhSHln11w7gZ1asmokcOdlgB4t8wIs2ZMd1oCOHb0qM5+SxZ/5rQEQB1FZrw//ohcmx0yNTTCxO+RI2KEoqZeQJTSxYvIsqWRa9FTnppF8U2bIi83DHl3oDRpVF93eXGxccMGJTezHfd0+XLEd4DnQuBwr4CyB8yAjPWoEFRSkZyHZJjwfuQtP7EvUFuQqF5QI6GcmQH8BRtHmxmjepWKmr7g4tezZ3Wahpxe8MJKFitkpHLkCq/YKcw6/muOGDZUCfun74X17tldWjYzZPAUbuH31kaqd+/a2WkJADsKlchfuZUdMVA3mXW8YBZGSiPtXFwzpGPRl8VdP1iDYnYqVqiAlDYDPW/OV9VxwcbUflAuGtIzuLyYPHGC6a/ShgwRjg2iLTjvaCOlvTh79owZ9CXN+4hMhoNGG+C+/UVhxptZFDXKvyCNcIQM3gELunZ8Q2t3eIE9g5rt35+LAp5sIvfdpk1OSwCrzQDmeN6rF2yK3sWc3wtsIdS5Ab5Um00bN+q5veuAq8z1M6dLo9kDe6Lx/i3+/FNVxzcYgQQYF7w7NrGIKnYzqKQaPnSoFor0+vNJe6CjCR71AgMVSeJ3S2JAFzGdRw1zL4YOGqjSwh+G07NbZzPwmzmfAuChWzV7XQeiFxinTP1IJi++WrtWr4lK5wUDlpnRK72v/HnFdGhDLf/sBcVaWD/yS+8zZ06rujBz+lSnJYD58+ZImeLFVCh4sdKoU+lTp5JWzV/X3xlE48eNMfZUZrV5jnqOp2gL9hFqnxfMrsVN3375xRdOSwBjRgWEFcLPC2bXpkYF9RrfDMwObduo2ukFKmMRI6z8Uhp1CUHjHbAAQhYzx+NAcIFW1bZVC1XPvKB+OzMgKrUXCNcqhsSo1F5gOjDr+vcSm2H6urwREt6dHXk/qHX+mRuHB5urR7dOxb1yfa+AB/TVuXO/RumwCBqpGLBIab/0RvdEJfCrfV06dtCp3OthgQzYEf369HJaAti6dbOee4tRhbzA3sIjhtTzglmrlDHCsXVcQG5ULQaQF0hypPfY0aOclgDYAxh7bO6syFVoqUqLc8GvalKPIjBgI3f+O0aYNDZ2oLceBTYITgK/qkkfQYZ2rSJLdUAqRxKj74cNH+a0iAww9hjS0u+lYlbo7JPeSGEECradFwgY+pZSa14wYJmlvMG5OnMbmwub+arH3kDQRTVgeZ5K5UvrrOnFp58sUmF17OgxpyWAqZMnS8WypXSXES+wx1izu3QxQqCSI4bKT9lsL1Clmbk/9wnrDya8rw6q33+/cbT/7SIopIKtGNu4gb3AlYt3Z+2ayC8SCYrdhYvTizmzZqrk9ao5nLthvdrybv/IahJkwPPjVzUxSLENPpo7x2kJYMZ0o2oakuCo8ALnBN4mv/Tu17uXSm8GkgucAKWM/o4DwAsGLAOT7XG82LhhvSO9IyIfMH5790DVbBrp3GDr1i2SOX0a+WTRIqclMiAner1rxzF7++tdLP78MykBGTyeK6Qw6goODi94ZjSL4WbQeoGEx76cMW2K0xIAz41D4PixyHYXazcITr80HzxwgNQ3M49XmlNOAKE0e2ZkVROnBWPCH8OIY4O+3bQxoHq5QLXDieOdYa6Zf66w9gKbFFOAmT8uEBRSUdDeTwb0baQXnjcvKJmMbcSL8AKPDeqgX3pPMlIOMnhLKzMY8cLUqlYlEhl4eQzYpkZ6e/V6HBu8GHRjLyA9njp/OTFsI4QBXigvOnd4Q9UyL7hO00YNpFePyI4CSI9DhIxfL1YsXy4F8+U2RIxsGwCECi737dsjzxouZhrBkCZVCvV6AWZL74Cl/0sWK3yd9J5tzsvMiPPDi/FGi0AwocZ48Xa/vprzdcVzbryGCBTu0QsGLGT40rfrJGSnDzd/G1G5lxkVYdW4fr1I7+eymenatWklHY2q6fW48W7RLt7q28dpCSCwvVFu00+Rw7RwtvCeUelcBLSfxup1jisEhVTETvkHJsbvtCkfXldnHLcsL92vJhEigvTy67aLP/tMUyS8oKMWfPSRGrVeoGLNmT3zOs8Wnkikrt8jh8OBWuZ+4LpmTcIPngeJ6gWqD0Gtfq8ZwoPj/aoM9hv9FRWmmfPgdvfbWS5QPbG36MOogLrLriJ+u5NdGv2zKGDmYfnAj9kzpsvOnTucTwHgtGC29zsh6MN5RivwRxcwS/v33IJUc2fPVhe3Fxj7OEn8eWBnz56VGVOn6tKEFzgxFi24fj8vlkiWLvnc+RQA18SjF12fxgaC6qiwuD2wlkfmrl+9dIGnq1rlCPXPIjRhSRViqF65kpQ1NiHqlhekd6R44TmZ9EFktdki9GBJFWJgjYswp7xGDRw8sL/aMAPeeUsXG1nktKXGQh+WVCEI1noIJcIBwKIjHjdqBkYVTWERerCkigEY0MTyedeYogMOlm83boy0yHm7IKQIgv15E9ePC+Ds8K9zxRZYb1q4YL5GQSQ0WFL5QN6MGy1A9AALwBT1vxHwdhJWNHTQu07L7QGvVcf2beXbTbE7qMhoZaH3ZpA7R1YNRI5tkJJDSFKh/Hk01ymhIeRIxWDivxfeRVLvukywwXVavN5YV/CvXr2mAa+s2p9z3OLe+/ADUhGBMHLYP9ue5loU58bFzI6LuKt57r/+uiJ/mRmR3+kjvxs7Knjv+WoU/cpCKYv2/mfjWv7zo46yVhUT/C53zsG5vedy2wK/R1zXPYa1vbQpk8ueXbsijYVAH0T//v3Xji+EDKlwE8+eOUPDYAjBJ57N7STiA/k8feqH0qp5U3m7Xx85fPiQfLVurS7GdmjbOlKYDYuZCz6ap4GWBHn6tw5FpSIOjqKTpCq4MWKfmFkqe6YMujjLugkBsOQIEcw5JixM742I+KgAqVhgfcvcGyEyPbp2ljf79IpkB0EQ1qi6d+6oIT0EGrtYvWqlTJ0ySe+XNIsj5u9wUrjJdV06ddBnbWdIQAgSfeSuDbJIyr2zwDlsyCBdO3JBwOr8efN0jYtNuzkPSX6AmDcWmwvkyaVrOYCNvsePG2uObaYzJf3IpnYgJlIhAPr17SWvN2qoyXzu+yBUacDbb0Wq58B7IxqEd45KSUQH77d1i+Ya7MuMnzJZUt1PmTU5jiPynf4nA4D4Sm9wMovehJ8RstWtc6dIAc28W7J5ibQgnca/5hUbCBlSzZ83V5PwCDuaYF5q4QJ5w6U+gzP580mkmek0XjgRGeQPkUpC+FKV8mV1JZ0wmTOnz0jdWtU174YIcKIdKLO8wInUYJM1NlwjcHOIebGs+pPkSCwZUQAErRK4u3r1SiUECW20ETnPgM+Y5mVZu/r6hVQWKklmpGRYz+5d9TkYHM0aN9LvcZETWEwiIYOMQZsnR3b5aF4gnIoYSfatIoKAwUxoE5sLkO7CQGDBnCgUfrYyf/v04w+rfXPx4gV9ljw5sun9EUhMUiKLrCBsxHuSJkVyjXgJBNRW0sRPno2FX/LEatWoqhER9B8BtI3q1VVhM3K4+VszY4xxotqZiaMiFcKvScN6GvvIQnjPbl01YRTVlTw1fmdgu+BZedcIPwb6i0meMc9aQyMfWLwmZSV96pTyofmdnDOEDH1FKg/nIYgWgQiI0axYppQ6c+gf+psA5gsX/tCAY6Ja6B+iRwjsJSQtpk32goGQIVVXI0mIH3OjAYg8WLRwvv5ORDhZoG4wJHZAsiRPa2AmQCoS0k/i2rKlS+SJhx8Ij3JHoSDkhsBbpHDpEkWlSsVy4WoEswCSmhhAQOQ0kQ2AFO+Chpze/CCIwSzkB6QqU7KYBue6M+y8OXM0q5n09Q/Gj9MMXwJjXTCAyZ5FxWEwEU2BZEU1unjposblEdbkBZEaxOUx03Ecwaqk2xN54qKVkegU6MR5guRngLqRIDwvSYTrnAiLPj27y7gxgWBiZn+I6Y12IauWxFBAGFlUpIKM3DskdDFz2jTNOPjll5PaB5DNBYO/YN5cmqM1ccL7Wj1q+bKlRgUOqH8QgMxfQLgbYVNeTQSB1aBOTf2dEm5ZMqQJD/u6eOGiDBo4QJMreTYEIkmVgMBr+oWk09hEyJAKlQDjlH2ccCfjLHDVMpLTkPoueAG8qF07AqE0xHoh1YlDYztPpO+lSxEeMwxxUrzxpjHovS8YoK4wgEHnN9rL+05yJDYVg8ob0zh2VJjOJH6g/vECSbBzQV4UZQL2GXK2bdlCc5C8QDVjcKHeMFCImHABIbinlV9G5BsR8kR0NwPKFQrMqqxfeaMsli9bpoG5zHYQpk2rFs43gXMguV0vHvUW2LfKBermvLmzNe+MaPdUZvYk+BdERyruhcGdwcziBcwsSTYznlBA6FRMpKKvIdA5I/BcYNNCUjezAUcR7zBsxHCdoXKbWbl504AGQKKoS3ovSD/iXbMkwd9QoYr3hoBhrPjtxWAipBwVkAiJTcIYMxN2A3izdy+N9naNWwInqTFAYRAAmerWrKYFPpBOqHNeo5WUb9QNUkdqGXXAHxRK9Haj+oEXQ0o+6idQUplZwZtCAqnI4vUjnFSeAFo8iXlyvqqzBEGhPJcXDGyip8n1QQ3ypmtw/15S/WHUGQYQyZ7etJPOZrZD7SQXyQWJmewu8uPu3Uqqvp7odGY6iOglFQQClD/j/KhMJGZih5UxM3vzpo31++hI5WKTUfdI9+ddvZLiRVW1UXtzZsukaqsL7DeXVNxfofy5NQDZhUsqljKYPQn65XiEztQPJ+ksTQYBgCiYBV7Qd8xwRPSj7mGvYa/zk3vCFvU6SIKNkCEVKhfGtovp06ao0wC9m+n/RqQiYh3jFZWQHTW8wbYtmzfVzkX6Y1tQYsoFqgGq4eiRAbuhfdtWansAalxAKuoeuEBNjIlUw4ZESP0AqbJroiH3jK3j3YyAbGPsAzx/pOd38pzXJRUODO4btRTBgLvZCwZJyhdfMHZeRIZzt84dpLiZ2emvUUa6cx0XflKhgrq2KzM2tqh3Xa6ssU/cARwdqbCbSMVw89oY0OQ/1TTvBIFEjpg3D4wkRPqFcmtKKqOOevPtXFIxl6D+PvvEo7LB4+jAxi5ibGFUbhwpZJvTRwBVun2b1jobtmjaRAWEF1zvy+WRkzeDjZAhFWnyqczgoMNRmxigDCoGRtdO7OaeKZxUeK1SG0m4xUkrYIYqV6qY7PtxT8C2KV5UVQoGMoRM/0oqI6UCyYZILHT4HmaQolLg9OAFMyuBbqadakWkoHBeEvu8UeFISX/6ByDDF2Pam8JN9Dbnwh5QQpcqruoI3kFULmL5XAlOKktLz3khFe58bENUpwfv+bfOdJAPFXPwu/1l+RfL1E4kNYZn4LyoYWlSvaTpOICiKN7sXfKZsF3dNHY8qcxq883g5D/nGWuECnlZJCOiLiHxUZcgFaklfuB9ZLbEWYRg5P5SJEuqzh3+bpiZvamY9N6QQSp0GOgEDjNTcSzVdr3R/DifMhnbhz6gxBh/y71wT/QbKjXeQQQUMxwlxRB0SxcvVgcQ61sIMgTQa9myqkdyiflbigMhjDlnbCJkSMX6C2oZs0iDunVUjXDzYkhcQyVz9WDS3pHA7gyCzUOu0cmTgSBUvketQW1gQEEu1l0A51i2ZIm6ZnkZQw1J9noyh7dv2yo9unbRTF6qJrGbhnfTgK+/+kodJX7ghUM6elMsqBPIrOfmMRGFjmeMSHPKXDEA3VkBlQRh4gKJi4MEQkMA8sRQU3uae8NR0smoPeRJAfLF8DjiDX2D8xqhw4AEzEg4b1xga9DPboIoKTecmwHPehzf1a9bSzOwuXdSKSA1Ao0ZBYdQVMCbiJu8jpmh8ASOMjP/r2cDRIEwI8xsCJnISdu6+TtVLekzMsVxTHjTVchno/8vXw60oc42bdhAPaPMqt98/bXaV+5yBc/gvm+WDOhnF2gzFMZBkDCDfxtFqkuwEVI2FUCie43u24E/+c6PuEitjgruYnKw4c/d+qeIbpGV9b0b1W9n1nI1Cj+uXImw+24VV/++agRFzOFaMT2/V72MbYQcqSwsEjosqSwsggxLKguLoELk/wAbs8ZWNmmwQgAAAABJRU5ErkJggg==)
A ball of mass m moving with constant velocity u collides with a smooth horizontal surface at O as shown. Neglect gravity and friction. The y-axis is drawn normal to the horizontal surface at the point of impact O and x-axis is horizontal as shown in the figure. About which point will the angular momentum of ball be conserved.
![](data:image/png;base64,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)
physics-General
physics-
A particle of mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is
Then the angular speed of the system just after the collision is
![](data:image/png;base64,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)
A particle of mass m is moving at speed v perpendicular to a rod of length d and mass M = 6m which pivots around a frictionless axle running through its centre. It strikes and sticks to the end of the rod. The moment of inertia of the rod about its centre is
Then the angular speed of the system just after the collision is
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of length
is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod are a and b respectively. The angular acceleration of rod at this instant will be
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMIAAACiCAYAAAATFRJrAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AADTuSURBVHhe7Z0FmJPntrb3Of/ZbYEWd3d3L+5eoLi7F/fi7lC0gnuLFKdYDac4LdACxSkOxYrD+t97JYHMdDIkIzDA+5wrV/dh8k0yyfe8y5611n/EwsJCLBEsLAxCnAhPnz6Vhw8fyJ07d+T27dty9+5defTokfOnFhZhEyFOhIcPH8qJ43/KD99vkFUrV8j2bdvk0sWLzp9aWIRNhDgR/vnnH1m3Zo10aNtaateoKoMG9Jd9e/c4f2phETYR4kS4ceOGjP9sjGTLlF6SJYondWpWl59+/MH5UwuLsIkQJ8LRI39I88aNJGaUiJI4XmypW6uG/PjD986fWliETYQoEX4/fFiGDhogObNkkkjh3pGUSRJKw3p15CdLBIswjhAhwiMTIB8+dFD69uwhWdKlkfixYkgsYxFSJU0kDerVthbBIswj2EQgXbp3z27p3LGdZEidQhLGiSnpUyaXlIkTSOrkSaRh/Trys40RLMI4gkUEUqVbN2+S1i2baWAcL2Y0KV6ogNSpUU3y5c6hRGhQt7b8/NOPzissLMImgkyE27duazaocf26Ej92dEkUL5bUr1NLJo4fKyOHDZVSxYpI6mSJpV7tmpYIFmEeQSLCrZu3ZPXKFXryx40RRRLGjaU1gw0b1snJ48dl1ozpUrRAfklpYoR6tWtYIliEefhMhMuXLsnCb76WSuXLSrQPwku8WNGlRdPGsn7tGpVTPHzwQObMmikF8+S2RLB4beA1EdALnTt71tzkM4zbU1iiRYwgKRInlLatW8mmTRvlwf37+rybN2/ItCmTpWDeDy0RLF4beE2E43/+afz/cVKiaCGJ+n449f+7d+kku3fulHv37jmfJXLj778tESxeO3hFhNu3bsnM6dMkR5aMEuG//6tp0oH9+spvBw7I0ydPnM9y4OaNG/rcwvnzSsoklggWrwe8IsL1a9dk/NgxkitbFsmdLbNWj/88dsz5U7/4+/p1GTNqpGTPmF6JQCbJEsEirMMrIlAv2LXzF5kxbYp8M3+eSikopAWEQwcPSZMG9SVOtMiSIklCrSNY0Z1FWIfXMQLBMP4/DTcBU0Dk8KFDMqBvH8maMZ1EfO//nmmNrMTCIqzDayIEhsePH8sfv/8ufXr2kIxpU0n8WNGs1sjitUKIEOHQwd+kR7euSoIEsWNIehNMYw1Ua2Qsgo0RLMI6gk2E/Xv3StdOHfSmjxsjqhTK96HUqlZV8ufO6dAa1bFaI4uwjyATgQb9vXv2SMe2bSRZwnjGHYou1at8LKNHDpfhQwZL6eJFrdbI4rVBkIhAxogsUttWLSVZgvjGHYouH5UuIUuXLJZjx446tEYFrdbI4vWBz0QgMN62ZYu0bN5UWzFjRo4oVT+uIAu/mS9//31dHjx8KHNmz7JaI4vXCj4RASnFVkOCZo0aSHwTFKM6rVm1sixeuEBu3Lyhz7l586aVWFi8dvCaCPcNCTb99JMWy4gHIEGt6lVkxbKlKqtw4W+rNbJ4DeEVEWjC+W7VSqlZpbLEihpJs0ONGtSVNatXyY0bfzuf5QBFN2KEIgXyWSJYvDbwigjXr13XrrPUyZJohqhJw3qyft1aHeblHwj0vvp8kuTJkc1JhJqyaePPzp+KPHhw/5lk28IirMArIqA1WvrtYmnWuKF0at9W1q35Tv65c8f5U7+4eOGC9Pq0m/YqUFSjsrxly2YNsv86d1ZJsXPHDo0lLCzCCryOEf7665zewL8e2C+3bgV8EzPjdO7smVpDiB7pfZVYNG5QTzZv3iQnThxXBWvF8uWVTPv37XVeZWHx6uE1EV6Ey5cvax8C9YQk8eNKlPfDSdoUyYwbVV9mz5opE8aPlQ+zZ5X//Oc/kipZIhk+ZJCcOnnCebWFxatFiBABazFxwjgpUbiQxhBJ4sdRzVGG1Cmldo1qJrCuJ/k/zCnxYkaX99/9r8SI/IHkzJJRRo8YJmfPnHb+FguLV4dgE4FZp9zQ3Oixo0WWdCmTGdeoiM41SpU0sQmas6rmKF6MqDrZol6tGlIofx7z3EiSJUMac+1wYxlOOn+bhcWrQZCJ8PjxIzly5IgM6t9XspobmtoC7Zkd27WRXj26S8VypXXqXdzoUfW/JYsUlC8mTZTv16+TSRPHS6mihSXqB+Eka8b0MmbkSDl9+pTzN1tYvHwEmQi/Hjggn3btotJrJtx9aE7+LyZNkD27d8vUyV9JmRJFdeYRQXP2zBmkX6+ecswQ597du3LGuEMMAsuXK4dOzc6aKb18NmqknDt3zvnbLSxeLnwmwpMnj2Xnju26CISe5GgfRDCxQUH5fOIEHfeCDAOtEf8WJzpEiKBk6flpN/nL7UYnizRhnCGDcaEIrLNlSqe9zmesZbB4BfCJCHf/+Ue2btksLZo2kkRxY2tAXL5MKZk+ZfKz9VDUB6ZPnSIljevDz+lWYyRkkYJ5Zea0qXL1yhV9Hjhx/LiMHTNaCufLo25StkwZZOzoUWoxLCxeJrwmAosBN6xdKw3r1lbZdQLj91euWF6n3l27etX5LIfEAiIUNxaBDFKW9GklferkqlQtWiCfTJvylapUAXLukydPqFv0YY5sKt/I7iSDu/WwsAhteEUESLB8yRINgHXMY8yo0qh+XVmxfKlcu3bN+SwHXFqjYoUKSNoUSc01ZaRW9aq6SorJFoXyfqiivEuXLjmvcAwPGztmlOTNmV2iRgj3jAxnz5xxPsPCInThFRGuX3dojdKmSCIpEieQ5k0ayg8b1gWoNbp165aJF8ZL7uxZJF3K5FpZJn4Y0K+3IUFuiWGCZ9o5Zxg36dq155bkz2NHZczIEVLQPCeqIVuOzBl1Fxs1CguL0IZXREBrtHb1aunasb307dVTV8cGRAJAwNylQztJEj+21hGoLKMv+v33wzJs8CDjKqXRLBNxwYzpU3X5IMBNImYYNWKY5M6WRWsSubJkkokmoL548YI+x8IitOB1jECQe+jgQTl29Kj8cydgEpw/f97EB5OlWMF85lR/79lco192bNefM/JlQL8+GjdEi/i+FC7gCKCvXL6sPwf8fiwD6VhmrDJZb8K4z5RgFhahBa+J8CJcMUQhSKaqjMSCLBCiO//LBH/79YD06dVDcmbNpG5SkQJ5ZPbM6Toq0gXIMHL4UCmQJ5chTHglw6Tx44yb9JfzGRYWIYsQIQKpU3oQSJkmTRBXkiSIo5VmpBUE1e4jHx89eqhzkHr3/FQypkmp6VUa/WcZMty84VC1MliYAHr4sCE6eBg3iZiDadx2i79FaCDYRDh96pQGx6RGY0eNbG7+xFLCECJn1syOuUYedqhhGfoay5ApbSqtPhcrZMgwY7pxwZ4H0Eg4RhgyYD1wk3CXJk0wlsGmVi1CGMEiApIIegzy5sqhFiBvzmzSulVz6dGtm2OHmiFCYHON9u/fJz27d5XsmTKq1AIyzJ0961mdARz543cZNmigeY3sWqVWKcfECdoAZGERUggyEc6cPi2jhw9TvVD8mNElU7rU6tf/sn27TJs8WbdrvqhnmWzUb7/+quMiM6RKoYW64oUL6Oop0rDgiXGT0CgNHtjfECa9yjbyGMJBBvcg28IiOAgSEY4eNS7L0MEaxOKysGl/6OCB6tcjw5g3e7ZPUywO7N8vvXt015ghRuT3pUSRQkoG94o1o+iHmdfInjmj1hmwEJDh/HkbQFsEHz4R4cnTJyqWG2JOZ0c9IKo5nbPLsCGD5ISz2+yWU2vk6zgXWjdRs6JEjRUlkor25s+Zo5VqFyDDoAH9tceBuAJXjCCdBYcWFsGBT0TAEgzo21uyZEz3THqNTgiRnGtxCDfutCAQATcJy9CtS0dt7kGwRxZq3tzZcufObX0OylcagQbSA2HeA2NlcM0mf/G5XL36XMxnYeErvCIC0moa93uYwBZJNbn9wvnzaE/ByRN++46pFAdnrtG+vXtMzNBF0qdKri2dpUsUlfnz5sj16881TYcPHdSYIVvG9OomUW/4ypDhgg2gLYIIr4hA4DrJ3PSkOuPFiqaBMCnTgPxzZNgTx42TXFkzKxGCskNt757d0q1TB61A09JZqngRWfD1vGdyDHDIkAHrRH0BwtAqOmXyl3L5ig2gLXyHV0S4f/++TDM3GfqgkkULyZfGL/ek/6H/uN0nLdW1cc018pUILC0nZkDblCZ5Em31xDJ8PW/uM40Tc5JIrfY3ZMicPrW6agwenvLVFybI9quItbB4EbwiwlMTJB/Yv0/mz50jy5Z8a2KCgOXRFNcQyeXPnUMih3/3mdbIXWLhC/ZhGTp31LEw1BnKliyuywzd5RhUqVW/lCGtSsRRtk41pLUVaAtf4HWwTD6fhn1PoNqLbBp/PVHcWJrVcWmNgrNDbdeuXdKpQzutU9DPUKZEMW0Gch88fPC3X6Vvzx6axo0R5QOVe5O5ck+/WlgEBq+JEBgoriGfZl0UnWj0MieOF+eZ1ujnYKyXfWDcJN3M066NbuCBZGVLFZcFxjLc/eeuPgc3iY2ez5cZMlEjj7aQulsPCwtPCDYRSGcytS5XtswmsI0iWY2LUqFsGW29DExr5AtIzO7evUs6d3DEDDGjRtReaSwDY+hdoErdr3dPtR7RIkaQIgXyKhkuX7Z1BovAEWQi4CrRVTZ4QD/JbG68+CZYLVmkkKY++/ft49ih9gKtka/Y+csO6dDmE61AMyqmnLEMixYu8DNQmDEzDCFmhAwrbouYAJ90rnv61cLCP4JMBDI2/Xr1eNZxRr/xlC+/0CHBtGHSsxyUOkJgYKT8HmMZ2rdppYE4bhiWYdHCb7TWAR49eqQBdK/u3SRD6hSSIFYMKVoov8ycMc0Q5nlcYWHhjiARgVOXOUXcaNE+CCdF8ueVzyeM17Hv7D7wVWvkE4yfxCJDYoZUJmaIHTWSfPxRGVm8aIGfOgOEdOiXHDJvxHyzDBmu2DqDRQDwiQictmRoSGmSEcIS6CjHiRPkwvnz+hzVGk3xXWLhK2j/bNe6pZIRzVOFsqVkybeL9fVd2L9vn3zatbNky5hOYpm4ggYgxHzWTbLwD5+IcMDcWF06ttfsDZkZKszTJn/lR/SmWqOXsEONIt/uXb9I209aSvJECbQ99OPyZeTbRQv1ZwDi/maI271LJ0mbMqkkjB1TxXy0htpFJRbu8IoIiN42/fyTtGnR3Nx08VUqXb5MSQ1Cz/vrI75x/bruSWAgcGgSASD0I4Bu19oRM8SOHlkqV/hILYP7ja7KVvRLxnrgJlEdnz1rhp+pexZvN7wiAh1jn40aIelScKrG0EFfbMa5GkDBih1qBM10rTmIEPqb97dv2yqtDUlRreKuffxRWVm2ZImfzT7UIrp26iCZVb8UWYobl27enFm2zmCh8IoISKTxrcuXLiXVK32s7ZQM/QoITLNgVDw3pWqN6vouuvMVuEK//LJdWjVvKkkTxNMBAg7LsMi89wf6nIcPH2lrKK6dS79UqlhhmUs3nHWT3np4HSMcPXJEVq1YIT9sWO9Rx4NKdeWK5VK54kc6x9RBhNpB1hr5ApqGdmzfJq1bOty3ONGiSNVKFWT5UiyDo+0TqLK1MzFDMofMu3hRJbaVY7zd8ClYDgwEyRCFIcEpkyaUSOHeUalFcLVGvmLbls3SslkTPfUJ6LEMK1cs80MGdjh0bt9WZeWxo0fRBqCv583zU6W2eLsQIkTgBkL7U6NKJUmdLJHegOT3yS4x+zQ4WiNfcf/+PbUMjK5PGj+2uknVKleUZcYyMFMJ4OoRQLPdk8WGCdEvlSiu6loGHlu8fQg2ERjFSCWZqdfsScP3RnxH7h6JBRYhtGME/0D+sW3rFo0ZGE1PS2eNqpXUMhDMu0CV2hEzJFWZd7lSJdQy2DrD24dgEeH8X+d0XRSpUkaxcPMTE3Rq304nUajWqE7oZ408YcvmzdK8cSMdRpwwTgy1DKuN+3b79nMy7N61Uzq0baMbQONEj6qWATGf+9AAizcfQSYCnWijRgyV/HlyqitEapXR7xt/+kmb6UNDa+Qr0B9t27pVmjZqoLokguiaxn1bsWypPHzk6K3ATdq7d7e0b/2JpHDqlz4qXVIbgDxN/LZ48xAkIhw+eFBVp8wlZdgvuwwG9uujQjx87LlzZkuhfHleORHAk8ePjWXYJM2bNJIkJl6IFyOa1K5eVVavXOknHti1c6d0bNdarQduEpKNBV/P95gmtniz4BMRdIDvoYOq7GTKBMUrmuaHDxmsuw1AUOcahTbY0dCkQX1N6dLcU7NKZflu9So/ZGBJIpINaiDEFcQMixZ8IzduWDfpTYfXRCBPv2cPbZNtNbjULjBz6jOu/awJmF1zjWihfBlaI1+Bm4RlIIuVME4s3fzDSquVK5cbgj/W5zA0YPeuXdKmZQtJliie6pcqlC2tlsG6SW82vCICpyaFtKaN6kvi+LElZuQP9AZhyYf/PWcEmS9La+QrHpsbftPGjdK0oSNmiGfIXKdmdVljLMOdO3ecz8IyPNcvURhEskHPgw2g31x4RQT85NEjhms1llOy2scV5BvSjP4WCQLSkwzbolHHQYRXlzXyhI3m/TSqX0etAmtysQzr1qzxQ4Yd27dL65bNdCEiOxzKq8x7kZ+hARZvDrwiApmVxQsXSL1aNaRF40ayZPEij6cj2zLpG06TLMlL0xr5Crb/bzaWgRoH85cgBJZrrbEM1CAAQwNoAGrdopkkSxhXD4BKFcrp53DvnmNogMWbA69jBCZVEHDiNnhSbHJaou2huIb79DK1Rr6CXgWXZSB4hhAN69SW9evWmnjguWWgAahNqxZKFlSrVT4uL0vVMlg36U2C10R4EegHXrl8mbpCECCSDvh6+Voj3/DUkPQHJSuqVUbQYBk2rPdLhu3btmmVWhuSDGEqlS8ry5d8a5t73iCECBEQtC1ZvFDz87RwcrpyenLjNGoQvLlGoY27xk3a+PNPUrdWTU0HO4aS1ZZ1a9f4cZN+MZawRdPGkti4SOiXqlasoC6ia2iAxeuNYBOBrTVIEqpXrqgp1QRojT7MpZv2da5REGafvmw8fPRQfjBWi4HFaKV4NK5fT77fsP5Z2pTsMA1ALv0Sm3uqVf5YG4DchwZYvJ4IFhGuXbumis3ypUvqzcO8obomoO7Yvq1Km1+11sgXUAdhkToJgaTOUx9J+Q8b/C5X34p+qQn6JYflq1KxvCxftsS6Sa85gkwE2jTZnI8uBxIkSxhf+4K//369brGhsZ+bJSzVEV4E3CTimTo1q0ncmFHVtWvSwFiGdeueFQzphiNmaN64oSQ2QTbWobqxDEtNzHDfukmvLYJEBKTXUyd/pXsLokd8X5tgunTsoCMXyRzNnT1bCoWxyrK3ePDwgRYP69aqrq4eGaVmjRrIj99/r0QBT5881QYgYoakCeKom1SzamUV87k3AFm8PvCZCBcvXtT9CAzZJbhEc8ScI/YmA26EGVOnhjmJhS9g4TlWgOCfCjSnPjEDi9Pv3n3uJm3ZtEmr7VqYM1ZRZd4rV1gyvIbwiQhsyJkwfqySgNOSqit7kplE7RoZz/b8sKg18hXEBViGWtWrSFxz4qdOlkRjgx9+2ODHTdq6dbM0aVhfZybhHvL8lcYykGmyeH3gFREYu37w4G8yZtQIyZ8nl+4tYzEHFWT+3R20baI+DSsy7OCAWasb1q2V2jWqqvWjzkA/NIU4V9qUFOtmtQwO/RKxRZ0a1axleM3gFRHwjadPnayj3+PEiKKTpgf07aOTLfwDGfa0KVOkQJ7crz0RAP0MVJuJAVCtMlWPQHnjzz8/ixkAVXd2QWAVEqNfMs//bjU9D5YMrwO8IgLqUzZo0oqZNWN6GTSgn/YfuApO7kCIN3bMaG3WocIclGWCYQ24SViG6lUqaaEwjXEJsQw//fj878JNImZoVLeOTuAmbqhbs7qsMpbBuklhH14RgS8SLT+roaZ89aXGBJ6wb+9eaWZOTNcyQYgQFrVGvoLpGGvXfKdDAOJGjypJjJv0SYtmxi3aqD8DuJCMxmxsLAPZJlSrSE78NwBZhD14HSxz4uHz3jW+sStYdAdkYeDu4AH9dRl4hHf+V4kQtrVGvoEK9NrvVkv1ShX11E+ZJIFahs2bfvYjtcACorqlKEdcUbtGdVlnSGTJEHbhNRECA0pOVjv16NZVg2jy6gTUr2KuUWiDngVu6mqGDDTtsPGTuaubNv7kfIajGw7LUN9YA4JsVeHWriVrVq2yblIYRbCJgP9M4IisgikQkSO8qzsL0qVKroW2hvVf/lyj0Ab9CGtWr1YyMCmPk59e561bNsuD+44bncMBl7CB6pdiGAsSXSUbuFfuDUAWYQPBIgL6GjIqzRo11B5fBHcM1m1k3CHSpxChfhhszAkJ0KzECU9/ArEAknPmrm7bssWP1AK3EP1SkvixtbmHLBoyb0uGsIUgEwESLFmyWEV2VF7JpnDizZszWz4bPVKKFy742mmNfAU3MylSyBAzygfGCibT+UgI81zAeuAaQgZSz7hJBNPIvCGTRdhAkIhw4cIFmTd3tk6bjmn8ZDJE5NAZs8ji8TkzZ0qRAvneiDrCi4DkYvWqlVK5YnmJFS2S1hE6tm2t81eZigEemRv+x+83SF3zWdDYw+fVtGF9PzJvi1cLn4lATzKV45LGBUJmwfQ4xGeuU5Dm/ZnTpr32EgtfQABMvYCeZuYhpUmWWNq3+UTJQLYNuGTeTM1g6HCyBPH08ODf/rFu0iuHT0Q4Z077CePG6rpWV52A7ZYM03V94aRYw+KAr9DGndu3lQxs+IwR6X1NGHRq30abeVxwyLw3qJiP/Q1sBUXZ+v36dRpcW7w6eEWE+w/uy769e2TYkEG6Ekq1RunTSu+e3XULjTvQGs2YNvWN0Br5CtwcpNjMQWLZOdXlzh3a6543VzzABp8N5saHDKRWE8WNKS2aNFJlq3WTXh28IgJB4eQvP5ecWTLol5c7WxYZ1L+fHD3qQWs0efIbozXyFZz6DjKU0VOfqYDsYYAMrhoC0hQkG7WqVVHLinuJZbBkeHXwiggUiJBWFPgwp3nkklEjhsmpUydVt+8ftG+OHjFCsmVMr67Tm6A18hW4hyuWL9VpgDQu0cLatZOxDDu2O5/hCLJxiWpUrexYqpI8icZapFtdknaLlweviPDk8RPdPcYoR8alH//zT+dP/OKp+T9mhzaqX0+nTruI8CZojXwFK3mXLf1WKpQp/WzGEw1M7GNAkwSQeZNGRdlKkJ04Xixp1aypH5m3xcuB18EyX96DBw8DVJwCfGC61JBnZ0mfRt5/5//pl/8maY18BW7OsiXfSnlDhlhRI+vIzC6dOmhy4aH5LAGfK2Rg7RaFuRTIvJs01kl87jJvi9CF10QIDHyZBM29P+3m1BpFlmgRI7yRWiNfQeGRxv7yZUrpZ5IxbSrp0bWLWk4X7hrCrDdkYDwMuxmoyLdp2Vw2/fzjM+thEboINhGwBLt++UU+7dpZK8lRIrwnGVOnlPSpUryxWiNfQcyw5NvFOvGDlbYsI0GgSCbOdaMjy0DZChk4SJBjtP2khWzZtNG6SS8BwSICX9D27dukU7u2kipJIokbM5qUKFxQGtWtK4Xz5X2jtUa+gswbk/E+KlNST32GHmAZ9u3Z8yy1SgVayVCpgi5mxLVkCDG9IHbwcOgiyES4/+CB9uq69ghQRCI3zqyjMSNHKiHedK2Rr2CCOGQoW6KYrtzKlC619DLu5L69u53PcMQVawwZGBxGkM2AhLbmM+aztm5S6CFIROB0IwCmQ4vpDdENCdiZwL+dPn1KZr9FWiNfQZ2F0fJlShaV6MRRyRNL7x7d5VcTY7kSEQTJNP9DBnoe2P3Wvk1r1XK5KvgWIQufiYCUABlxk4b1VIdPDpxcOKcYX6RqjaZPf+skFr6AzwgylC1ZzMQMyDFSSq8e3TTh4JJakFpl4WHlCh9JbOQYJq5o17qlbDdksDFDyMMnIty5Y8z2qlXSqF5dSQYJokVSd2j9unVqJcDbqjXyFWwhYh1VmeJFJGqEcJI5fRrp06uHIcN+5zMchw6WoVL5cmp1WXLI5s/tWzcbNyngNLZF0OA1EZhwxxKQ+rVraSsmUgv6clFPup9QLq1RWNyhFtbAFO1F33ytzUzot9KkSCJ9e/XU0ZmMlQTEDCuXL1cyxIwaUXs/EPOxwMS2fYYcvCICWQ3MNF8GTes6Nr1BPe3TdWU8XLh185bKMfLlzmmJ4AWoMyz8Zr6ULlbUUWcwblKfnj20OOkKju/du/+MDMQMyDFojYUMNmYIGXhFBGYVjR4xTLNDpPWaNaqv/bkB+apXrlyRoYMGSsY0qfT5YXGHWljDtWtX5Zuv50upooW1DkNlfkDf3nLwt1+dz3C4nCuXLZOKH5VRN4n0a9eOHVS/5Knab+E9vCICwR1pPxrUKZz9/CPCsH+n8gjwuOnZUknrposIb6PWyFf8ff1v1XGVLFJIor4fXts+B/br42eGFDHD8mVLpWK50hpkI8dAv7Rr585/WWYL3+B1jMBJf+SPP+T0qVMBdlSR8sNKdGrXRidYfPDu/ykR3matka9gw7+SwVgGYoZMaVMrGQ4dPPjcTTKfM4tJKpYtpX3SaVIk05H8kMHGDEGH10QAAQ32AhTXiBewGJhslJScWFZr5DuuXr0iX8+bqwXJyOHfk6wZ0unQtMOHn1uGW7duyvKl6JdKKmHohuvetZMqW62bFDT4RISAgLkmc9SqeRNduYT/Si8Cp5lqjYxFsDGCbyAmYzhCsUIFJMr74VS3NXhgf/n998POZzCP9pYsVf1SCf3MmbqHZGPv7t227TMICBYR+DJQTTKehLoCQjG0NLQeFi2Y36E1egsbc0ICNDjNnTNbLQNkoM6AZfjdWAbXqY+LuuRbh34JC0ydoXuXzto7QkuohfcIMhEooK1auVxnGVFhprbQrHEDWbRwgUwY+9lbMdcotMHEkLmzZ+mwBCYIMo186KABJlb73fmM5/qlcqWKq36JbjiHfmmPR1fW4t8IEhEw3RTXGHuOZJixLlSbyWtfunhB5s6aaQtqIQRihrmzZ0rRAvk0tUo8MGzwAD/94tQivl24UMqWLC7RIobXA6hXj+5yYP9+K9TzEj4TQU+gRQt1uBcTGBh/zrAq1JEAd+ltm2sU2mCD6RxzuGjM4KwzMFHkyJE/np36Dv3SQimnZIigSYvePT41ZNhnU6tewCci/H3jhiyYP09VkYnixZaEjCJp2lhn99y/56hw3rx102qNQgFIXGbNmC5FCuSVSOHfleyZ0suIYUPk2LGjzmc49UsL0C8VM4QJpwmLvr17yK8H9ls36QXwmgjUD+YYf5WZPXRZMYKEdCnu0JOnz1N2FIbelB1qYQ2XL1+WWTOn62cbKfw7Wr0fachw/M9jzmc4LPbCb75RyQaFOVLY7LpDv8QaLIuA4RURMK3IhksULaRiOya0dWjTWlN1/sGeZUR3lgihg8uXL+k0kSImBosUzhFAjxw+VI4dPfrs1Hfol76W0sUhQzjJkCaFQ8x34IBNrXqAV0RAUcpGTbqlkieOL507tPPoe/LcLyZNlDw5s2llmdVJlgghiwvnzzusrnE/I4V7R3JkziCjRgyX48efj9lR/ZJWqQtJ5PffUzeJCSOHDv5m3aQA4BURSJWyB6xPz09l+NDBsmvnL86f/Bt0qDHZjeJaisTOuUa2shziuHTposwwZGDgGm5S5nSplQwnThx3PoOY4ZqjSl20oAbZHGQDnJKNJ06Zt4UDXscImFsWjlPo8ZSFuHrlssw2PmzBvLlVawQRrNYo9HDx4gWZPuUrXQCPZchmAujRI41lcIsZ/jYB9DeGDKWKFpEoxjJQZ+iPstVYhsfWTXoGr4nwIlwxgRwzT0nx0a+Ab0p7IaPPrUUIPfz11zmZOplxnA7LkDNLJvls1Eg5dfKE8xnmgLp8RebPmSMlihRSy4D1GNi/rx/90tuOECEC4+K//HyiTsqO9kF4He1CUcdqjV4OLlw4r2TIlzuHkoEha2wtItPnwrWrV2X+3Dla8Xe5SYMG9JU/fv8dNaXzWW8vgk2E06dP686E3LqVP6p+GdUrfSz5DCkggm3MeTnAbaUzUAPo8O9KjiwZZdxno/1YBtzaeYYMGkAbMjB1b8iA/vLH4cNvfWo1WEQgMP5s9CjJkTmTzuBh+jNLyYcOHujQGiVLbNOnLxHnzp7V8f35P8yploHx/RPGjpEz5rBygVrE3Dmz1IWFMOy5GDZ4kBw98u8R/28TgkwEKppUNknLxYjkIAETF/hAZ02frh+0rSO8fGAZJn/xuXFTsykZsmfKoCJIdzKgX5ozCzLkV20ShTnIgGTj0aO30zL4TAREXPiVQwYN0KArTrTIOsmZ5nKySWheIIKVWLw6nDt7Tr76fJIjgA5nLEPWzEoG95gB/RLiSOTyNPdkzZheBg/s99ZaBp+I8PTpE/nd+JMUZrAE8WNGVwUqCy8Q24Hbt2/LjKlTLRFeMbAAn08cL3lzZlMJ94c5ssqkCePk3LmzzmeIHD92TPr06mlihdSa7s6eOYMqCN5GeE2EB+a0379vryoa0yRLIonixNZF48zxd++VpbLsrjWqX6embPz5J+dPLV4miBm+mDTBkMBBBlKrkOOvv/7SnzMlgyXprMSNbOIFYouVy5fpz942eEWER48eyu7du6Rzx/aSNmVyFdy1+6SVjoMXf5k3tEbu6lOIsGXL8wXcFi8XVy5fkWlTJkvxwgV0wSHqVSzD+nVrZdCAfsYlSieJ48dRRfG0qZNV5fo2wisiMF1hwrjPVAdPJoh9YAi4AqowU9YnnZorWxZJnjiBxg/MRaXB/8nTpzqQyj5ezoOWTmI6po+MHTNK9V+IJnGBEO1lSJNSuwsrlCsjs2fOkJMnT6h1D+h3va4PZm/xX+7VwDRWXhHhn3/u6NaXrp066CJBBHeeQBsh5jZpgniSOF5s+TB7VmnWuKEO/RoxbKgMGTjAPl7SgzT26BHDZfiQQfqdQAR2M1BDIKOEO0RjFRXnLh3ay+iRI1SiEdDvel0f/fr0ksHG8q1d851OIvcEr2MEJq1dvHBBbpr/BjQyBLZRXJs4fqzkzJpZ3jfBV/RIEXTCAlkJHtQaXHNTmZiHqaYSTXN6QA9kGvQ+xHVew5gYRh7SgRXQ83nQt8uuBl6HFlK9htd50TXu7808HK/j+b3xcL2O670xGTzQ1zEPPg8ybfH9vM6Lr2Fgmuu98b8Du4aH63V4Pp+D6zr+Tn7GSHr+y/9P47/rf/t/Hf6d9xDQa/DgO+bv5vt8fs0L3pt5bffXod2X1wnoua4Hfy+f1b/em/nuAnq+6/Hu//xHIoZ7R7oYt/68MzYKCF4T4UU4dfKkalzy5szuvGEjOm6OZ284vP4x/G8e/G/HB/yelvz/9TD/HuA1+ocH8Pxn1zg+tFdzjZM4nq4xPwv1a8zD/zU8sATuRHd/8B1Basc1zuu8fp3wz18nlK7hZxyYPl3jfLxjiPDBe/81RGgnf50757xb/40QIcKxo0e0U4qRI/yhuEOtmjXRBvK+vXo4TFTvXlKnZnVtJOELYUobKlU27iDv5tHr0+76IDM1oE9vHV/CUABSta4vMU+OrNLS/O7+5ufu1/C/+bf+xhS2bNrYxCiZ9YPiSyZwZ20rz6NBxXUND8wm6eBG9etoXMNrcEPkzp5FF6G43hvviefzX16DOgpja2iZhPA8KF41bdhAf84gX9drOK7prfNM27RqoTIUbjg+A16nScP60rN7N+nb2+97G9ivrz74ewrkyaViRsiRJUMaaWau4Tn+3xu/A5eo3SctJW+u7GoNYpsTl6b/urVq6PviO+nldg3fDfJs5PPFCubTk5cbDs0S6XHmJeFiuN4XD/4Wvp/2bT4xrlVBHeWDq8UMpgZ1auvf86/3Zl53mHlvrBornC+PJDRuGVYLKU5NE0v2Ns/T78fPe+up0/66deqojUasJ4NI/D3En906d9LP2/U6/h+MxOzZvatmw0jkeEKwiOAorh2WoeZGz5wulabo+APxM/fs3qkyYQLtq1euyJbNm6VHty6apWDbPKk65Bk0ily+dEkfuF4XL1yUa1evqRSAyW19evTQaW9cU8gQh3EmrGdFXvzsmotcc1UVsPyMKmnObJn0y6SohJ+8Z/dufS6jK13X8L5oYGHDJRkUcu3xY8XQNCPFJUaiuN7bJfN8rqMQxXX0AfOlciNDHlKUEH/71q065YP37+d1zHW//bpfJSgsbocIvA432NYtW4zZPq+/W68xnwHvk99Di+W4MaOlqLlB+Qx0ql2XTrJj6xZ9rp/3pn/PNa0Qfz5hvF4DEbKYz5wb9vv16/V9kUnifXGN43Wua5F0+pTJ5mYrotYDHRLE2LB+naZh+b2O92auMb+Dz58DkG7ECuVKa6yhy0w+aSU///ij/j3u7831Oif+/FP7KMqWLCHxzd+DLLy5OVBQJVxy/g3P3pvzddjr/fXcudomHNsciEwDb9W8qawy15w6dUo/J9fr+H9ccP6XNoLAJnoEmQjECYcPHZSB5jTlj+GkQvD15ReT5OSJE35aAvlDkGMw4iVezKh6Qk/+6gv12QKKN8D5C+dlzKjheqolT5RACpoTkcwH1VFP/RCXL11UrQ2/H0vA+yFVSOcWi/oCAu+BjjpuAPYco88ZOxqx2kmPbY188KhtSUWmSJxAScckOkasPLgf8GAtDgSm15Uyr4NPzOswiYImGbIaAYEDgblGlSp8pNYgk7k5sZQM+Xrg4Rpm0NKMwzpbFMDc0JyK+/ft0zW2AeHe3Xt6Ylap+JGSGsvOoUV6nP0MAYHhYlxTv3ZN3dmQOlkS5+vsNb8v4MWH9D8sX7pUqlWqqFYABWybli1kx7atOjExIPAd/LBhg1ozDgKmc7Rv/YnWryjehhSCRASUigfMB4vpQ3JNBqJYwfzKdP9+GCX7EUOHqjo1mjkFsQRoYWCqJ5w+ddKQYKQ5ZbPoyVkgby4ZP3aMEswTkCJ/+fkkPdWjGP+dE5pT8eyZM85n/BtnzpxWEnBD4w6h2ES+7K7L8Q/aJL8yZC+U70O1ODmyZjKuyAC1jJ5AShltTxFzQuPbZk6f2nwmgwOVM3DCzTXXOEY6fiDpUiZXF+YIsmkP4PSEBOVKlVT3JoNxU5hevm/vXucz/g26D5lRVbFsaU1mUPvBlXBffesfuBgrDAlqV6uigXKKRPE1GA0sm8jrrDCvU/XjCsa9cWwMZX3uju3b5amHw5BU7oZ1a6UWr2MOtsTG6mDZthmr6+nACSp8JgJvjpGCfMBMSCAVx5bIOTNnqElzgQ+RhvKhxk3hBsPHz5s7u95EmD9PwAyPHjlMchh/mw+MOEJvTnPTegL9EF9MdFRQIWV+4w5NHD9OCRUQyHCdPXtGrUWBPLk1K0V3F33ZgQVUV4yp/9IQBx+fv4dTnQYXXBFPoNmemURFC+RXtSdxhM4kcptW5x9X6PSbMV1KFyui2Zi0yZOq7+w+1Ms/qOjjPpQy18SJHlV1YKS795sb2hNu3rgpy8zNiWCSYBT//lNjCXAjPZHAMYB4iVSrXFFP6KTGGnRu307rSp7guqaScW2wOIymJP7attVzoRXirF+/VmpWraSxFJaXqSlbjYsdGlO/fSICZgq/vasJXFIbf5DTrUzJYtokzgnmDr5o+pu5aQhu8uR0kMCdLP6hJBg+TANdfFv8b+IIbtqn/kvYThCHfDkJS5BNg2OCaQRmp4z18FRAOWtOfCwBUnFSh1lNUAgJzgRiPSAvZCNo5QZAvjyofz85duyYx5tG55cymKtgAWG0CgVJx/zSwx6vgTjIpCsY10a38BuXg91qWAJPbiQuAi5UmRJFja8eW4uenTu20zjGkxtJbUgXj5Qro2nTNMZN6WpcG75fTzeawxIs1b158YwbybbPjibwxe3y1PbJ71q6ZLFULl9Oi3e4Ufj3O3ZsMy5hwEsR+Xcq37WqV9HsI0oGiMMQudBapOg1EWAo602ZYJE4fmxDgnB6kixetEC/cHeoO2RigpzGbYAs+Yyfj9uC++IJuD1jTFCLC+W6Bktw4vjzZnT/OG/cFGISTuZI4d/TrA9VbXeVpX/QQ/EV/r2JV/gbCN7ZBsS/ewJWgvePdVIXKnMGvaFpaPEEh9R5hsZFEDRT2pQa6BOUeipwckjMmzNb3aFoH0TQm7Nvz55+pmD7B8H+/HlzdMJdDHNypjWnLZYAq+0JEEfdIUMC3DtO2+7GwmMJPBEHi7PSkKBmtcp6QnNTs74qMLeL2hOvw1TEONGi6Ou0btVcB8J5IjU3+rq1a4wlqKwkIDYi0+ZYuh5620S9IgIfDm+kRdNGWjHmBKnycXlZtmSJicafp6RgP30KI4cNVRLg16F+xJ0gWxEQsDL48dQgcmTOqGnI/LlzOm5OD64NH+K5c2dMYPyFtociNcbyjPtsjJzwEEfwOueMZeGGptkd1yarOdVHDR+qFicgPDavg6XTZhfznrgmZ5bMmm715NpghdS/Nyd0cR3e+56mWIeYYNp9+407sA5kSObNcdzQfAYEn2oJ/gjY7eJ1XCNbypQoYq6Jon0FZHoCmjflAnEEQS5uCvl43BTH1p1fArRSfNZYAq6pYdwUrCGp0o7t2ug6XE9g0BhxBOtxcYdYaELam2UynoCEnyyVWgJjDV3EYfeGp4RCSMErInDiU35nKgW+ZDXD8NWrVuof6w5OO0iAj87z8hh35cvPJwQeGBs3ZaRxh3CDcIdyGQKR7iRgDci1wUXCEuBm0Q7K6+TOnlnGGhfquLEenk4aXodr2EbDKZg5XRolgSeyAU7oLyZOVCUtNwD1DOoBkN2Ta0OakJigeKEC6hKSgaEWQHbIUxYK927e7Nnycbmy5gaI9GyILy6Up7+HjZxMHmTwL1KWlEkTOt2UPfLQg2uDJVixzPjqFcrpjcaycyz8TkMCT1koJY5xoerUqKYZPwR6LD/ft2ePx7+Hk3vp4sXmsKyglgPitGjiGA3q6VTn3zesW6duF3UP3CGIs9GQgExYaMMrImDiyHrUrlZVdUOYO1wld9w3fwj+MIExJW0lgbEEdEx5Arldll0UNAFr+P/7H71mjL9xJP6Bb8sYdPx71wgT7c0NJKPEzbRyxXJtQokY7l29OSEsKVJPID3I6VSmRDGJ8N//dd7Q7DQ76HzGv4FFRNOCy8HsUU5b0qpYAte62IBAvwZZG4JpsjYUgl70Ojt37DBuShXtI4A4XcwNTQ3FE/gMuBEb1autrk3ieHE007PbkMCTOwT2mhseBTGk5obuYCzBnkDcLn7Xwd9+k+bmPsElhKTc0Nu2bPF4eACsC6lUV3GytYkJNm3c+FJIALyOEXBf+CBJm5JH9w9unBnTpugsf25sCkf+A2j/IADFtFcoW0oLXyOGDA705gQIp/CjiU9IexKQB0Yc8PjJY/l2EZOiSxiyZdeb80wgcQRQd8CQp3rliipW692zuwlYPfvqQE9CExiSJyeeoIpLwfBFIDDEynKI4KYc8uBCucDNQY9Hw7p11IKSVw+MBICb8IcN66VJw3rq5rVt3Uq2b99m/j1gi+PCDvOcBnVrq3tHuhMSeEpCAFwY3KxPmjdT97hZowayadNG5089g/izTcvm+t64hqLc/RBOkQYGr4nAicJJ5InV/DtzcpZ+u0iWLf020FSfC5jwE8f/lK/nz9Ut9KcNCQL7kIH6+ufOqv9JMMpp68l9cIHfSVEPPxdCHPz1xWMPHTHFWX1f8+fNlaNH/gj0RAO8D9yptd+tklkzpmkg6cl9cAd/z7q138mCb+brTcTnHBh4H8RcK5Yt1VqDZodecA1/L9VtZkxR79lqbjxv/G6qwwxoW/D1fE13eirKucBn8Pff181nsFql3WSh7npwh9xBME5qdPrUyfoe794N/HVCGl4TwRvwIfDhsmb2RTeaOxhnHtCmzsBwz7wOkoQXkcAF3g83GKm5Jy84Bd3BF4Rr6AtY20TWyBsSuMBz7927G6ib4h9Yx8CkxQEBEjGR8EVkcwfXYO18uYZ4hDjGF/Ad8d48VaZDEyFKBAuL1xWWCBYWBpYIFhYGlggWFgaWCBYWBpYIFhYGlggWFiLy/wEaxVZyu4LA5wAAAABJRU5ErkJggg==)
A uniform rod of length
is sliding such that one of its ends is always in contact with a vertical wall and its other end is always in contact with horizontal surface. Just after the rod is released from rest, the magnitude of acceleration of end points of the rod are a and b respectively. The angular acceleration of rod at this instant will be
![](data:image/png;base64,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)
physics-General
physics-
A uniform rod of mass M and length L lies radially on a disc rotating with angular speed
in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc. Then the kinetic energy of the rod is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJUAAACOCAMAAAAPbbolAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAALlUExURf////7+/vDw8Pz8/O3t7crKypSUlNvb28TExI+Pj9/f30dHR7m5uenp6ZmZmfb29oKCgl5eXouLizw8PDAwMOrq6ry8vGtra1JSUtjY2FhYWOzs7Do6Onx8fEtLS/j4+Pr6+jk5OZWVlcLCwjg4OL+/v4qKitfX16ysrEZGRt3d3aqqqoSEhLe3t9ra2qSkpM7Ozuvr69zc3NbW1ujo6Pf39/v7+/T09MnJyXt7e1FRUSoqKhcXFxgYGBoaGhYWFiMjI29vb5eXl/X19Z2dndDQ0LOzs319fURERA0NDQAAABMTEysrK0NDQ1tbW3JycoWFhZOTk5iYmIeHh3Z2dmFhYUpKSjIyMhsbGwMDA2RkZCYmJlBQUHV1dQYGBgkJCUxMTOHh4fn5+dHR0bq6upycnGVlZSgoKEVFRZ6enggICMHBwebm5m1tbRQUFE9PT6urq+Pj4zQ0NCcnJwQEBFRUVCkpKXp6evLy8nR0dBAQEN7e3v39/WxsbFlZWXBwcICAgNPT07a2tpCQkGBgYE5OTj8/P0JCQoODg66urlxcXHl5eZaWlqOjo7S0tL29vcjIyNTU1M/Pz6+vr6enp2ZmZj09PUBAQIaGhlVVVWhoaMDAwM3NzYGBgTU1NaampoiIiElJSTc3N42NjcfHx01NTeLi4rCwsDMzM5+fn1ZWVufn50hISO7u7tLS0pqamldXV3FxcXd3d+Dg4NXV1TExMe/v7ywsLMzMzPPz86mpqS4uLqWlpeXl5fHx8TY2Nn5+fsvLy39/f7i4uF1dXS0tLeTk5Hh4eNnZ2QUFBbW1tbu7uyQkJBkZGcbGxmdnZ2pqajs7OyUlJW5ubhwcHJGRkR0dHR4eHqioqFNTU6GhoQICAnNzcx8fH2JiYr6+viAgIAEBAcXFxcPDwyEhIbGxsSIiIj4+PkFBQVpaWi8vL46Ojl9fX4mJiZubm7KysqCgoGlpaa2trYyMjKKiopKSkgAAACT0ZS0AAAD3dFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wDuZjaTAAAACXBIWXMAABcRAAAXEQHKJvM/AAAGSklEQVR4Xu2czZXrKgyAXQGFQCMcl+Q+WLBjyUYbVvRAH9TxBLEzmZmbIAF28s69X85MkvlxZCEJib9lHoCPTyMKuUQn93cfgtQJ3OLs/vZDcH6JeZE+7e8/A2MXaWHxYX//GQS9LGJZPH59ENHH5KTSH2buKiQpPs0H//F/BmSsD/iIHgelUUHn7QFtRJI34USsT9cCKNC6rl7b4ISqDxeM9tu6ZoMSQcYIdjEy+HW1LsWfjQYyCZPXzQu3Xtz7SLNuVj23IpDOb3m9uKtOObQMu+jyYmXBrxAOP/wPTDG3t0R69MHkjNFae3/7ssYJjBD779+ARB/UxQOFUilhuIpJoRuiF+IPxS8vuILorMfQFP/URCCVQ3GNuFawiB9q3WttSGW8N+kqwUDorGlmnKzP4Qo3BJc9I4cCYbM5u+MB5/WL2PlHovGnygXC2572kEaH0wJX0l0yFaTxbn85F7zwSPWStD7B7JW3g43g2l0nEwhZ7S/7kVpPtXqp/RRrDXliCSvyrCpdZTOrFd2E1jvAVpyidTB5qjXYGWKB9ZMDsxm/oPS+ZQjKBOcc45PCqPJB66Z1Jqy2rE3SkAOaGxMLm4/iMqLUfXJdyZ8VSJd9RsiU2wdfShm50aVC2+oXy5GEWgRWq5iwbCvDuXR3pZgyqT+FXOs+mRm6Qv12BmZJDJ4pYBIvSgtyAhH16j+xZn/RRJkFeHaFqC5HZPiJK/JzpVpCO+j8IjFu5SYVy64KmtwYB8BJPEOXrvA+uNmpowyIwV6nhuJPfKkw+vLaMJJ6ULHHM9MpFWheEmhJ0eRwI1PqF75dofGyUlxFU+2hK1ul4utq1zIVTYtw6pCqNMSXrhjGAoxcq+YABO5SlZu460oaRrNU96VBNcJDqqrau67CynAtSVaWoEb13a6gVsWHrtS6rQzXIvdrmjokcOiqTuqirsoTeB/8Rg+PkdiHqExtALFaY437piuVlUuZMdRBC0KLIRtgtBYz9iBvUt10tQAY1hCyItkLsHsnqMMHd2tHqeozESBN6tNkf0QeUt0uD4FmKQektiG28wOxVsN98QpJBDVwou1OHNMV+HZPQo3rD+y6Ouyq6Ark74mepxCakNEF3MCMvcbyB11J6dE7yWNC7VwAiB3zF1jJ54Dx6S6VNJB8iomcPLV7HVq69w2L5SB6yKOuYjEDQy5Em/ILfk0b1zXj0zddbcYY+iBoc3UUKw3b0bU3/mZXWQRGX9iKDVBTJSbJl+/fdIUtyCgVZCNRvnW0LKRyQeFVH3VVb55ee7dyX8nubtCvbR1HB7XPzmG8gtKkkZ441BT7ObfGGIMb25FaUD6n1uaDSP78VsMJG0KTAP5sYPGOF9R6cxBmflVoGM4Uqfh21QgNDWcgEE0MMTCjXnzt+szhiEeSqaLE1TrLKb0K8FpX7IzhjsI+usriVs1eStRqwW6pDEp18yS9btxQDK8ntLunu1FFNZ9BIn8lsnw9DzZgV8Ef08rswNAqFsZ9sIuGD9bxsetpWPuMKNpBQ1cz+sEOGv3gjJyhg0YR2lFMzKChjBlZXwcNc+4YZZhBI0x2VBMTaOriLWG0VXnxBz9m0BwHogxxTac5VEQflZ8HYRyIPNg+j9gyq2ZpdgaEGdK0zzdcCKV5CGOncyHNmZRNZJdCmuKOVzchzb8u9kKiFkganQfRYviLH0agzExU6EPSE3DU4VPZtdqnD8ZCiwsTB8a00YVdNKdYv0xZrOqFNus6DnMui7sGqZPA9PZLAjx7go23BqkT/hR3z1pAJoK8nOMOnLRV5YvY07N1/RODztvuUDAH29nbGnuiWK7XnbpXMBMQ/RmAPE0sNbJtJc7c1fNAGrvuOWLF0V1HQ6p+QsrDKQlrNRyJCUJNUPcP1DblNqWfGbfELJOQ8zZVQZjYj83a9zdrH+KOmrJ7E6+yv5qEHN/sKqfutLwBwQ/tWS57pc9Ib4e2FkfbP9HeQOnO2XKU6cTMFoTW7EMXINqxxm+D5sE5cgD/Qdl8skwVobOlKiwFn/mLebqAGMopFa0PgxRQfu65CUMk4711zyWL5XwN/YYjulI5j8QaoeLjSTLlPKByWJE2ZQniW5DJBVuPkSkHyRhbz5Xx1gSUdP+TtwHlHBnlBKLSW0+4+StZlv8AbV0HXk4zN6cAAAAASUVORK5CYII=)
A uniform rod of mass M and length L lies radially on a disc rotating with angular speed
in a horizontal plane about its axis. The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc. Then the kinetic energy of the rod is :
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJUAAACOCAMAAAAPbbolAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAALlUExURf////7+/vDw8Pz8/O3t7crKypSUlNvb28TExI+Pj9/f30dHR7m5uenp6ZmZmfb29oKCgl5eXouLizw8PDAwMOrq6ry8vGtra1JSUtjY2FhYWOzs7Do6Onx8fEtLS/j4+Pr6+jk5OZWVlcLCwjg4OL+/v4qKitfX16ysrEZGRt3d3aqqqoSEhLe3t9ra2qSkpM7Ozuvr69zc3NbW1ujo6Pf39/v7+/T09MnJyXt7e1FRUSoqKhcXFxgYGBoaGhYWFiMjI29vb5eXl/X19Z2dndDQ0LOzs319fURERA0NDQAAABMTEysrK0NDQ1tbW3JycoWFhZOTk5iYmIeHh3Z2dmFhYUpKSjIyMhsbGwMDA2RkZCYmJlBQUHV1dQYGBgkJCUxMTOHh4fn5+dHR0bq6upycnGVlZSgoKEVFRZ6enggICMHBwebm5m1tbRQUFE9PT6urq+Pj4zQ0NCcnJwQEBFRUVCkpKXp6evLy8nR0dBAQEN7e3v39/WxsbFlZWXBwcICAgNPT07a2tpCQkGBgYE5OTj8/P0JCQoODg66urlxcXHl5eZaWlqOjo7S0tL29vcjIyNTU1M/Pz6+vr6enp2ZmZj09PUBAQIaGhlVVVWhoaMDAwM3NzYGBgTU1NaampoiIiElJSTc3N42NjcfHx01NTeLi4rCwsDMzM5+fn1ZWVufn50hISO7u7tLS0pqamldXV3FxcXd3d+Dg4NXV1TExMe/v7ywsLMzMzPPz86mpqS4uLqWlpeXl5fHx8TY2Nn5+fsvLy39/f7i4uF1dXS0tLeTk5Hh4eNnZ2QUFBbW1tbu7uyQkJBkZGcbGxmdnZ2pqajs7OyUlJW5ubhwcHJGRkR0dHR4eHqioqFNTU6GhoQICAnNzcx8fH2JiYr6+viAgIAEBAcXFxcPDwyEhIbGxsSIiIj4+PkFBQVpaWi8vL46Ojl9fX4mJiZubm7KysqCgoGlpaa2trYyMjKKiopKSkgAAACT0ZS0AAAD3dFJOU////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////wDuZjaTAAAACXBIWXMAABcRAAAXEQHKJvM/AAAGSklEQVR4Xu2czZXrKgyAXQGFQCMcl+Q+WLBjyUYbVvRAH9TxBLEzmZmbIAF28s69X85MkvlxZCEJib9lHoCPTyMKuUQn93cfgtQJ3OLs/vZDcH6JeZE+7e8/A2MXaWHxYX//GQS9LGJZPH59ENHH5KTSH2buKiQpPs0H//F/BmSsD/iIHgelUUHn7QFtRJI34USsT9cCKNC6rl7b4ISqDxeM9tu6ZoMSQcYIdjEy+HW1LsWfjQYyCZPXzQu3Xtz7SLNuVj23IpDOb3m9uKtOObQMu+jyYmXBrxAOP/wPTDG3t0R69MHkjNFae3/7ssYJjBD779+ARB/UxQOFUilhuIpJoRuiF+IPxS8vuILorMfQFP/URCCVQ3GNuFawiB9q3WttSGW8N+kqwUDorGlmnKzP4Qo3BJc9I4cCYbM5u+MB5/WL2PlHovGnygXC2572kEaH0wJX0l0yFaTxbn85F7zwSPWStD7B7JW3g43g2l0nEwhZ7S/7kVpPtXqp/RRrDXliCSvyrCpdZTOrFd2E1jvAVpyidTB5qjXYGWKB9ZMDsxm/oPS+ZQjKBOcc45PCqPJB66Z1Jqy2rE3SkAOaGxMLm4/iMqLUfXJdyZ8VSJd9RsiU2wdfShm50aVC2+oXy5GEWgRWq5iwbCvDuXR3pZgyqT+FXOs+mRm6Qv12BmZJDJ4pYBIvSgtyAhH16j+xZn/RRJkFeHaFqC5HZPiJK/JzpVpCO+j8IjFu5SYVy64KmtwYB8BJPEOXrvA+uNmpowyIwV6nhuJPfKkw+vLaMJJ6ULHHM9MpFWheEmhJ0eRwI1PqF75dofGyUlxFU+2hK1ul4utq1zIVTYtw6pCqNMSXrhjGAoxcq+YABO5SlZu460oaRrNU96VBNcJDqqrau67CynAtSVaWoEb13a6gVsWHrtS6rQzXIvdrmjokcOiqTuqirsoTeB/8Rg+PkdiHqExtALFaY437piuVlUuZMdRBC0KLIRtgtBYz9iBvUt10tQAY1hCyItkLsHsnqMMHd2tHqeozESBN6tNkf0QeUt0uD4FmKQektiG28wOxVsN98QpJBDVwou1OHNMV+HZPQo3rD+y6Ouyq6Ark74mepxCakNEF3MCMvcbyB11J6dE7yWNC7VwAiB3zF1jJ54Dx6S6VNJB8iomcPLV7HVq69w2L5SB6yKOuYjEDQy5Em/ILfk0b1zXj0zddbcYY+iBoc3UUKw3b0bU3/mZXWQRGX9iKDVBTJSbJl+/fdIUtyCgVZCNRvnW0LKRyQeFVH3VVb55ee7dyX8nubtCvbR1HB7XPzmG8gtKkkZ441BT7ObfGGIMb25FaUD6n1uaDSP78VsMJG0KTAP5sYPGOF9R6cxBmflVoGM4Uqfh21QgNDWcgEE0MMTCjXnzt+szhiEeSqaLE1TrLKb0K8FpX7IzhjsI+usriVs1eStRqwW6pDEp18yS9btxQDK8ntLunu1FFNZ9BIn8lsnw9DzZgV8Ef08rswNAqFsZ9sIuGD9bxsetpWPuMKNpBQ1cz+sEOGv3gjJyhg0YR2lFMzKChjBlZXwcNc+4YZZhBI0x2VBMTaOriLWG0VXnxBz9m0BwHogxxTac5VEQflZ8HYRyIPNg+j9gyq2ZpdgaEGdK0zzdcCKV5CGOncyHNmZRNZJdCmuKOVzchzb8u9kKiFkganQfRYviLH0agzExU6EPSE3DU4VPZtdqnD8ZCiwsTB8a00YVdNKdYv0xZrOqFNus6DnMui7sGqZPA9PZLAjx7go23BqkT/hR3z1pAJoK8nOMOnLRV5YvY07N1/RODztvuUDAH29nbGnuiWK7XnbpXMBMQ/RmAPE0sNbJtJc7c1fNAGrvuOWLF0V1HQ6p+QsrDKQlrNRyJCUJNUPcP1DblNqWfGbfELJOQ8zZVQZjYj83a9zdrH+KOmrJ7E6+yv5qEHN/sKqfutLwBwQ/tWS57pc9Ib4e2FkfbP9HeQOnO2XKU6cTMFoTW7EMXINqxxm+D5sE5cgD/Qdl8skwVobOlKiwFn/mLebqAGMopFa0PgxRQfu65CUMk4711zyWL5XwN/YYjulI5j8QaoeLjSTLlPKByWJE2ZQniW5DJBVuPkSkHyRhbz5Xx1gSUdP+TtwHlHBnlBKLSW0+4+StZlv8AbV0HXk4zN6cAAAAASUVORK5CYII=)
physics-General
physics-
A uniform rod of mass m, length
is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
t along x-direction at point A. The x–coordinate of end A of the rod when the rod becomes parallel to x–axis for the first time is (initially the coordinate of centre of mass of the rod is (0, 0)):
![](data:image/png;base64,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)
A uniform rod of mass m, length
is placed over a smooth horizontal surface along y-axis and is at rest as shown in figure. An impulsive force F is applied for a small time
t along x-direction at point A. The x–coordinate of end A of the rod when the rod becomes parallel to x–axis for the first time is (initially the coordinate of centre of mass of the rod is (0, 0)):
![](data:image/png;base64,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)
physics-General
physics-
A uniform equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction
. A horizontal force F is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is :
![](data:image/png;base64,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)
A uniform equilateral prism of mass m rests on a rough horizontal surface with coefficient of friction
. A horizontal force F is applied on the prism as shown in the figure. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling, then the minimum force required to topple the prism is :
![](data:image/png;base64,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)
physics-General
physics-
A small block of mass
is rigidly attached at ‘P’ to a ring of mass
and radius
. The system is released from rest at
and rolls without sliding. The angular acceleration of hoop just after release is –
![](data:image/png;base64,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)
A small block of mass
is rigidly attached at ‘P’ to a ring of mass
and radius
. The system is released from rest at
and rolls without sliding. The angular acceleration of hoop just after release is –
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lowermost point of the disc
![](data:image/png;base64,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)
A uniform disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lowermost point of the disc
![](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-
A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in figure. The coordinates of point of application of forces is given by
![](data:image/png;base64,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)
A planar object made up of a uniform square plate and four semicircular discs of the same thickness and material is being acted upon by four forces of equal magnitude as shown in figure. The coordinates of point of application of forces is given by
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown a ball rolls without sliding. On a horizontal surface. It ascends a curved track up to height h and returns. Value of h is
for sufficiently rough curved track to avoid sliding and
for smooth curved track, then:
![](data:image/png;base64,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)
In the figure shown a ball rolls without sliding. On a horizontal surface. It ascends a curved track up to height h and returns. Value of h is
for sufficiently rough curved track to avoid sliding and
for smooth curved track, then:
![](data:image/png;base64,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)
physics-General
physics-
A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved?
![](data:image/png;base64,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)
A smooth tube of certain mass is rotated in gravity free space and released. The two balls shown in the figure move towards ends of the tube. For the whole system which of the following quantity is not conserved?
![](data:image/png;base64,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)
physics-General
physics-
In the pulley system shown, if radii of the bigger and smaller pulley are 2 m and 1m respectively and the acceleration of block A is 5
in the downward direction, then the acceleration of block B will be:
![](data:image/png;base64,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)
In the pulley system shown, if radii of the bigger and smaller pulley are 2 m and 1m respectively and the acceleration of block A is 5
in the downward direction, then the acceleration of block B will be:
![](data:image/png;base64,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)
physics-General
physics-
A uniform thin rod of length
, mass 4m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O & perpendicular to the plane of the paper?
![](data:image/png;base64,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)
A uniform thin rod of length
, mass 4m is bent at the points as shown in the figure. What is the moment of inertia of the rod about the axis passing through point O & perpendicular to the plane of the paper?
![](data:image/png;base64,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)
physics-General