Physics-
General
Easy
Question
A rectangular rigid fixed block has a long horizontal edge. A solid homogeneous cylinder of radius R is placed horizontally at rest with its length parallel to the edge such that the axis of the cylinder and the edge of the block are in the same vertical plane as shown in fig. There is sufficient friction present at the edge so that even a small displacement causes the cylinder to roll of the edge without slipping. The angle
through which the cylinder rotates before it leaves contact with the edge is
![](data:image/png;base64,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)
The correct answer is: ![c o s to the power of negative 1 end exponent invisible function application left parenthesis 4 divided by 7 right parenthesis](data:image/png;base64,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)
Related Questions to study
physics-
A uniform circular disc has radius R & mass m. A particle also of mass m is fixed at point A on the edge of the disc as shown in the fig. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R/4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about PQ. Find the linear speed of the particle as it reaches its lowest position.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAL4AAABmCAYAAAB1GSvfAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABb7SURBVHhe7Z0JeA3X/8ZvLC1Ka28VVZRWtVL82qI7tbWqWqTUGktbS5WqIggiCUpT/duX2GsXS8RObbU1BEESIbGEaERELEES7/++Y87tTXKTJjJzl+R8nuc8ZGbuvXPPvHfme853OQZIJHkQKXxJnkQKX0fuxMchJjZB/UtiT0jh60YK/L27wmXIH0hUt0jsByl8vbgdjC6v5oOhYiscjE1WN0rsBSl8nTjlPwHtWn6GaiWKwXX2UXWrxF6QwteDe2fh1e8nbAk+jpEtqqDs270RkaTuk9gFUvg6cGHbFPQdORcPjP+PWD4ATz9VHuO3Xn60U2IXSOFrTcoNTPuxA/qMW45TJ4NxfOdM1ClqgHO3KbipHiKxPVL4GhMfugE92nwFr2lzMW+uL+bN98WgNq/DqWQDrAu/rR4lsTVS+Bqz+f8GwWPJMfWvRySeWYf6JfOjyejN6haJrZHC14iHyXcRsXs2Gv/vI0w/fBkPUtQdRu7FBKLLG/lhKOgM373ncOu+2U6JTZDC14iHif9gw0xP9OkzEHM2Hkb8fXWHkahjWzBhRH/06fUdPKb64cJNs50SmyCFL8mTSOHrzN9//43FixcjNjZW3SKxB6Twc0hKSgpu376NEydOYMWKFZg0aRJGjBiB3r17o0OHDihTpgwMBgPeeusttG7dWmmdO3dG//794enpiRkzZmDTpk04f/48HjzgzL/EGkjhZ5OkpCSEhYVh3bp1+Pnnn/Hxxx/jxRdfRPHixZEvXz5F5NltTzzxBEqXLo1XX30Vbdq0wS+//II9e/YgKipK/VSJ1kjhZ5EjR45gzJgxaNWqFZ5//nmLAhatWLFieOmll/Daa6+hSJEiyrbKlSujWbNmeP/99/H6668r70HBp32teatZsya6du2KmTNn4vJl6fnVEin8TOAd19fXF02aNDGZLObtueeeQ506dRSTxtvbG+vXr0dQUBBCQ0Nx6dIlxb6vWrWqcuzAgQNx584d3LhxA9HR0YiIiMCpU6dw8OBBLFq0CIMHD0aLFi3w8ssv45lnnkn3WfzhuLq6YsuWLYiPj1fPUPK4SOFb4OTJkxg+fLhiwqQVIG31Xr16KT8ImjyZwR9O9erVldfx/bJCYmIi/vrrL0yYMAFff/01qlSpku4c3nvvPcyZM0f5EUkeDyl8M0JCQvDDDz+gYsWKqYRWqVIlfP/999i2bRtiYmLUo/+bs2fPKiYP32PIkCHq1uzB9+CsUMuWLdM9Cd544w1MnjwZCQkyyyu7SOEbuX79OsaNG5fOdqc9PmvWLGX/40Bzhj8avtfQoUPVrY8HZ4/4w+STg+aQ+Xm+88478Pf3V4+UZIU8L/w1a9Yo5ou5kJo3b47Vq1crNnlOoNkyYMAAZZC7a9cudWvOiYyMxMSJE1P9AAoUKICOHTvi9OnT6lGSzMizwo+Li1MGnAULFjSJx9nZWTErKFgt0Wt+/urVq4rP4NlnnzV9B45LOFiWZE6eFP6BAwfw7rvvmsTCOfRRo0Zly37PKrw7825/7949dYv2BAYGwsXFxfR96E/o06ePLt8nt5DnhL9s2bJUd0j+APbv36/u1RYOOmk2FS1aVJkF0hM61qZPn57quzVs2BBnzpxRj5CYk6eEzxkQ4VCiTUz7W88YGs7IiMHtoEGD1K36Qt/Bhx9+aBI/nWX0FUhSk2eEP3LkSFNIAe/AnK3Rm3PnzqFatWrKZ+Z0Vic70MHVrVs3k/jpaAsICFD32gfJybYtuZInhE/7XYigfPny2LBhg7pHX2wlfEJhceDLJxs/v1y5cti+fbu617bwSdiuXTslBOT+fdvkJuR64TPgy8nJSbn4dCYdOnRI3aM/thS+4LfffjOJnz/6ffv2qXtsB73SPJ/8+fMroR22IFcLnwNKdjAbnVMMBbAm9iB8QqFRZDwPzv3beq5/9OjRJuEzHNsW5FrhU+QlS5ZUOpg27p9//qnusR58pIt4H2sNbjOCYxyeB1ujRo1sGubAPASeB30oFy5cULdal1wpfIbw1q5d29S5y5cvV/dYl3/++cfkFZ4yZYq61TYw5KF79+4m8TP2iNtsgRS+DnBQ16VLF9MFzmpUpF5wKnH27NmKpzg1yYgOO4xFv3vBbdhQjPYahwm/jIPnWB+sP3BWPUZbOHXboEEDpV9oZixZskTdY12k8HVg1apVpmnLTz/9VPPwA+14iNvXL2O5x6fGcy2E72b4Yce2TRjfuxlKla2KIYsPQo/78bFjx5RBLvuH448rV66oe6yHFL7GXLt2TclaYqeWLVvW5oM4Pn04q8I8W2ZwWeLsVnc8Z6gO33A1IO7+OfSo5QRDDVeE3X74aJvG0JHHPmKjyWNtpPA1ZtiwYaYLyuhFW8NEFJFIwnOzxOkAN6Pwq2HGSWEKxeDH+oVgqNYJITpVHOTcOXOFeV6FCxfG7t271T3WQQpfQziDQicNO5QZSjdv2r5Ea3h4uCn1kKmFlqDwyxmqwGd/JOKvXcKmqX1Q4Znn0XvWHuMoQD8Yn0QPNs+NCe7W9KRK4WsIB7HsTDprWObDHsjKPH7IRneUNzyLru5e6NWqLspWa4iZO07CGuX0RVjDk08+ib1796pb9UcKXyMuXrxoyp7irIW91KfJivBPBwwz3vGrYtKB09gytSdKFq+GSbusM+A8fPiw6a7PEAJrIYWvEbTn2ZFsS5cuVbfanqwJ/5GNPyvsrvGv6/i1fU08+UJzbI+yzmwUK0Tw/OjsY5K9NZDC1wBOVzZu3FjpSKb42VOpPo47RLJ5RjZ+xHZ3PGu8488Oe+RJTbm8Gy2qPImqrcYgygpm99atW02xTOPHj1e36osUvgYw6IwFnNiRtg4LSAuzr0TIQvpZnRRcizyByX3fU/a39VqO8OhH9XLObfJCOScD6rYZjPW7g/FAxx8AS5TUrVtXOQeGMuQ0zzgrSOFrAKsjsBNpq+7YsUPdah8w3dDNzU0JW0if5ZWC65dCsdPfD6tWr8T6zftwPkbEzyTi+K51WDRvMbYdCtVV+IRmGPuwUKFCSiKL3kjh5xDGmtA7y06sVauWHXtp7RtWZxOZaQyv0Bsp/BzCejdi7r5Tp07qVvuC5QSZ/WQNE+Jx4bhIpEiyTKHeSOHnkJ07d5qSLKZNm6ZutR+YAkgPKefJWfjVnmFBW/YjQz70fnJ6eXmZhM+paFvg0MJnLXp2IJs1bNPsYotk88fF3d1dOU+WO6fHWSsobKZAchzB0ur8UTErjp/FatGsDcQnjp+fn9JHLABA/4LeOLTw2VHsQNaUtNWdIzPsJQMrKyxcuFA5Tw5wtUza+fXXX5X3ZeOTj/U+a9SooUyhMjSaFSH4N+/+4rgvv/xSfbV+OLTwhfOF8/eMzLQ3HEn4nBHjeTKk+48//lC35hyGQghzNKuN0aN649DCZ916dhT/tcrgMek2oi9fUjK8omNuqPHyKRnGzTuS8IODg015uczR1RJmn2VltRjOLHFpJGvgsMLnHLkoA8g4E1YS05OI/Ssx/Md+GDTEHZ7e4+BjHF+MH+OB4Z5zkFGdAEcSPscjJUqUUM41oxDqnCBmcjJqtPdZ899aOKzwueCaSKNjlWA980dPrx0D5+q1MWzhXzCFyCfHYa2XK+p93BvBGfzm7CnZ/L9gSXNRfjCj8IqcwBvTt99+axJ62ubj46MeaR1yhfA5h6+X8JOjd6FZxaKo18sX6WI+78dgzZxZOJQ2nVaF4w7Wruc52vt0pt7CJ5zeFQ5H88YKENbGYYXPaTEmnLDj9DR1Aqe5wpC/DDz9Ldd/uZcQh/hMpr2ZcsjS47du3VK32CcUvijHwulHvWABKa7uKETPFWhsUe3BYYX/8OFDNG3aVOk8Dm75BNCe+5jbqz4MRapjXiDDhnMv9DCLwS39I3py9OhRvP322/jmm2/ULdbHYYVPxHQmvY36TGfex5xv68FQmMJ/PG8mpwk5sKWNz3VxzRu3eXh4pHIYMSaed1xLx4vGeBrhXeXdkqu6cI0tS8fyfZidxnVzBewr2tTiM7ifC82JuzC9uJx/N/eNsAY/j8vovPj5nAYV58UnMP+2dDy/308//aTUNLWV49Ghhc9O5IXS04F1cHIn42c8A/c159Qt6UlJtlwNgTatqPqQWeMiDoK2bdtaPCZt40J0hKHP9LZaOsa80dchlgnlD8fSMWmbsPWZ0fbJJ59YPCZt4w+EcL0uS/vTtjfffFOaOtnl999/N3WgXm7upKgdaFquAKq09MA/6rZ/uYVjB/chItby+IIJ3AxLpvi57Ocrr7ySqnEbPZnmWWMsX85tlo4Xr6FpJxZ8YKGqnj17Kt5P1sW0dDxtaj51REom+4oTA+Iz+Fph39OjysoQjNFniAGhWcm+ZgSspfPi53I7V2YURWAZQMgkdu6zdF7cxvNiHU1b4NDCp2tdeAWnTp2qbtWeMwHjUOv5smjU0xu7jkci1nhRYy6cxNoFs7BkUyAS/uOGRTFw8MgCqeaN8/wsM5gWbrN0PBu3372berxBYTLKkXd/S8dbehpysM3P5zHczxUe2Y8UJOsRWVrpUSxMnfYz+Lncnna5I97Juc/SeXGbLcNMHFr4vNuJJHPa+3py9fgmuPftinZfd0LP777HMM9JCDgQirvWf0prDicGRBkUVl7ICzi08HlH4TL4vGBc8ibtnVCSNZh3y+A09qM1ElHsAYcWPhGph0899ZRpwCfJHpyRYR8yejJHsywpD3DtcgRCw84g/EwYwiKiMy2KlfwgxjgIvmgh1ikZF04F42JmDpIc4vDCZ7K5qA3DKTJJ9qAtb55sniN/yIMEbPVxhXP91pj+x0IMdnWBm+9uZPQcvn58A5ZuO420c2I3zq5H2wbNMPeYfhG3Di981oEUjix7Ky/iCNDMEY4rLcqLnN/gjc87jlUqwYXM/gpV6/fDeYvLXCViz6qVOBSZehCdHH8ZG5d44IumX2NxUPqBv1Y4vPCJebKDrWq+OypaF5SKDBiLZp9+g1U7tmL8gG4YPmsn7lpwczyMDcaKNZtxJdUDJhGBWzfgUOhB+Hzf1yh8/RaozhXC53RhxYoVlQvI+Wk9VxHPTXA+n2Mj9ptWJQQjA8ahxRffwW1gO7zv4oGMnr+Rh3bAf/sRmD8Mog+vxBA3b/hvWwzXxk0wdN7O/5wqflxyhfCJyBllwoOtlv5xNFhRgX3GWHitVkO8YBR+a9cJiLoVjuEuTTFsyVF1jxnJN7Fn4zLsUcom/kvUkc3w8RqNseN+RsPXa6Hj6IW4otNqoLlG+HTGcJE3XkiGAgv3vMQyTAkUoQ4uLi7aRLcm3cKWCZ1Q4y0X7L6SguuBC/DJ+40xdvlexJk9hBOvhcNvyVpEZ3g3Pw/Prt0wP/Cq+rf25BrhEwY/8UKyMZNfYhkGkomFIZjut2vXLnVPDkm5j+iI0zh6/CSibz6ayLwcehRHQy4g0WxeM+nBbVyPyyxM+z6uXriI63f0CTUnuUr4dPUznoQXtFSpUlar/uto2HopIHsgVwmfsD6LqP5r34u/2QYmxgiTkJWcbbH4mz2Q64TPgC2x0gcboyMlj6CzSqRrckBrT2sJWJtcJ3zCyEOR68pCRXJuP/UNgQ6rvH5D0ET4rDMzb948pX7l9OnTbd5YFax3794mjyTtfcZ9+/r6Wjw+NzfWqZk7dy66du2q9AUbTR2uIsNyHpZeY802duxYpY4Pk/Et7Tdv1Be/i8hFyAmaCL9Hjx6mTpVNNr0b1xvIqZNSE+Gz+i1LU7AgEV3f9tJ4p+e/5p3G8Ft6eUuXLp3u+NzUeD2YqyAG+mx07vF7i36xReNn87w4xjC/Lmy8NtyX2flxX5cuXXLsd9BE+LQfT506hYMHDyrRkvbS6JI/cOCAUoFXdC4vPM0eni/zQy29ztFbUFCQci24orrIUOM6AjRH+Z3ZL5ZeZ4124sQJJbaKedLimphfG1Z44DGWzpHfieevxUxdrhzcWkKENLBxuX+OA3IrzK3t16+fSfQVKlTA5s2b1b22hSmKzs7OpmuRtjEPl6mPeuNgwn+I5KQHGRZp/S9YvFQsFMdG501MjH4RgLaANWsYV28upPTrb9kG9rWYbcusMbxciwFsZjiY8JMQdXIXxv/UDZ+1/Bw9+/6Igf37GP91w5pDWVtShg4ukafLVq9evVQ1ZxwZzuAI5xTbRx99pNxh7QF61S2VD8yoMZWU8Vd64XB3/Ad3E7BtVDMYnCpg4tpghJ/5Gx5f1UHh0m9g2p9ZEz/txw8++MDUyQzWoinkqF5MemMZViy+D30XLM3HZHx7gcWjxPmJxjghMfh++umn0+1n3SS9cEgbP3LhN3Aq8z+sPK5mMYQvxasFDKjZ0QdZvdQUBat8mc8u1K5dW6lzyXo4jgB/qKxuxkGh+A6siZM9h90d7F/nC0/jgH+Mx2i4DXXH7LX7jVu1hdXeKHTO3HTu3FkZaLNglaibP3/+fKWxojLr7rzwwgvKtdALhxR++LwecCpdB0sDVZnHbkaDogZUazs2w8SHjFi/fr0yLyyEwztQw4YNsXr1aty8eVM9yr5gPRpGn4ra+2xMFGfV6LCwMPWoLJB4AZP6tkSjNgPht/cITgSfwKFNi9C9WX181m8yLqcrD50zWCrR/PzE8kNsrN0pYP0eUZhKLxxX+KVqY9lRhrYmwH/0FyiYvwzclh9/dEA24ere9B7yLiMuBBvXZ2K5DXqm7QGaNDTJKleunOo8WTWaP+DscQsr3VqgREXjayNSO4NuBM2Hc4kiaOWxEXqG+LFqnPgOHJRbE8cU/sJeKFisInoO+w2TxruhY/sumLB0L27nME2NdyRWahB14kVjebzu3bsr5UusaTfT5KI5Q7OAtSvTnhdLDdKNzx9udrl3bhPeKesEZ1dfC7NkcfBqVQX5yjXCjiidcv+MSOFnk/B5PZGvlDPm7j6P+BvxuKvxI5krmXA5HNqa5kJj4/Rg3759lcc0L5bWRaxYyZiJIaxVyQGr+SyNaByYM+4oISFBfVX2CdvgidLG92rrc0DdkpoNw5vA4FQWv27Rz+SQws8mZ+cbTZ0ydbEiSF8bnPUdebdlMVRRu8e8UZQ0MyhQZn8tW7ZM8RTzycEnAxekY0wJS6Cw8f/0OrJ2Daf36Khh/U+aU/3798fnn3+u1LgRy+ubNzqh+IPjKularAUQtHIwihnft/N0y4Lb/Utr4+cWx2i/f21vrZHCzyaRC7rD8HQtLD9mnVVG6AmlSL29vZXa8aLOpKVWuHBhZWqOMy0cfLIMNmPg6bipX78+6tSpoyz6zLgTOtMsxaywcfaDpkz79u2VpwsXQtaSi9snobyTAc09tqtbUuM/rDEMhSphxr70xWO1Qgo/yyQh6tQeuLvUgaFAcXQYORcnLlp/5oWmECs5MKa9VatWivmTkYCz2uhL4CohnOpjYactW7boWhwrJfYw2rxcBOU/HoH0I4RrcGtSCaXrdsdpPRaaUZHCzzIpuB13BaHGu29oyCmcPhOB67d0qj+RRWjC0GzhNN3GjRuVuHJGq9KBxFVGWNSWTwlWe2vevLliNjE2ns4ZziQtWLBAqXhAs4rmEQP+rEMKjiwehAqlXsCINamnQEP8RuKVSjXgHaDd0v6WkMKX2Ih72DN/FL74rA3cJs7ESj8/LJjiia7tOmCiX2C6mpZaI4UvsSlxEUfhM6A1yhQ2irBQTfgGWWfsJIUvsQPuYLvx7v9BrUp4p707jkVpHbSQHil8id1w59JxLJ46Hl4TpmJFwF5cidfYSWKGFL7E7rgbH4trcTdxP0k/S18KX5InkcKX5Emk8CV5Eil8SZ5ECl+SJ6GXWwifuQbWRApfYjMYzUrRMxo1JCRE3WoNgP8HDvDW/slW6xwAAAAASUVORK5CYII=)
A uniform circular disc has radius R & mass m. A particle also of mass m is fixed at point A on the edge of the disc as shown in the fig. The disc can rotate freely about a fixed horizontal chord PQ that is at a distance R/4 from the centre C of the disc. The line AC is perpendicular to PQ. Initially the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about PQ. Find the linear speed of the particle as it reaches its lowest position.
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of mass mass and radius r rotates along an axis passing through its centre of mass and normal to its plane. An unstretchable rope is wound on the disc. Tangential acceleration of a point P on the periphery of the disc when a uniform force
is applied on the rop is
![](data:image/png;base64,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)
A uniform disc of mass mass and radius r rotates along an axis passing through its centre of mass and normal to its plane. An unstretchable rope is wound on the disc. Tangential acceleration of a point P on the periphery of the disc when a uniform force
is applied on the rop is
![](data:image/png;base64,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)
physics-General
physics-
A uniform disc of mass M and radius R is supported vertically by a pivot at its centre as shown. A small dense object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is
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WkOb9IkSJyPrR8+XLjisYROtq3a9dOirFly5Z6meMV0CIMB62ANNtzDY3eKlxc15bBF0Pn7WbNmkkx0utHOwFEHS1CB3bv3i3X9zjfoceKXid7eRYvXiyNVnRKWLp0qZGreR5ahAL6VH777bcoUKAA2rZtK9f9NK8OQ/vTgkwHc6450sVOEzkeL0IOo7gTgy03LX+amIP+rnTRo1GLa6qaiPFoEdJ3k71fx44d9RzGifA4gbx588qN2jpA1H/xSBHSYZq7GAoWLCgPXNE4H1pROVfkGisX/zX/4nEipBM1KwN3NWhzumvh5mSOOvLly4dZs2YZuRqPEuHKlSuRP39+uY1IH4riPrhPMleuXPIIOI0HiZBuZjlz5pTzE437ob8tG8RevXp5fLh9jxAhW1wKkJtaNeZh7969KFOmjNxk7MlR2mwtQvp4sqWlBZTHgGnMBx3jGXaDm4mtsvcyprG1CClAer9oa5y54cGlPCuSW6U8MZqbbUVI52suQXAxXmN+uH7IoFRM9LjxJGwpQsZ4yZMnjz740mJwNz+HpjyBOLLwjHbEdiJkrE0aYTZs2GDkaKwEw2cw6jmdKTzFamorEXILUo4cObBs2TIjR2NFGF+VcW24mdoTsI0IaXyhJ8b06dONHI2VYWBiTik84f9pCxHS+Zrh+Rg/U2MfuK5Lx2+7x7GxhQg5f+B2JO2hbz/oYkhfX2dHKXcnlhehn5+f3Dxql3ifmmfhGR61atWS8WseP35s5NoLS4uQ8wbOAxlSQWNfaKhh7Bo2uHbEsiJk/BduR9LzQM+AO/M54rFj6BHLipBnJjAQr53nCppn+eyzz6SzNw9OtROWFOG5c+ekTygPwNR4Dpz3szdcsmSJkWMPLClCHsLCAEJ2axE1L4ahKBkTli5udsFyIly1apXcmsRTbzWeB31KecApTxu2C5YSIX0JGSiIOyQ0ngtDU3JYypCKdsBSIly0aJE8mssT95xpnoX7D3v06GG8sjaWESHnfzwViceTaTSMlFCsWDG5M9/qWEaEnAvyS9cnxWoIpyb16tWzxdzQEiLkqUgffPCBx2xt0UQNLlVwehIUFGTkWBNLiJAbdLkuqP1DNY48fPhQ7sTn4TNWxvQi5FyQUZu/+uorI0ej+ZfJkyfLcyTp6G1VTC9CWkLLlSunz7rTRMilS5fkkNTKx3WbXoQLFy6UMUc8OTis5vnwzPzu3bsbr6yH6UXIL1jvlNA8DzbUdGW7e/eukWMtTC1CNdTYtGmTkaPR/Bee9kQRWnVfqalFOHXqVOknSCuYRvM8OnXqJMOcWBFTi5AWUbu4JmmcC9cMeeT5jRs3jBzrYFoR0lueEdQYS1SjeRGHDx+WAaEY8sRqmFaEPDaL4/xDhw4ZORpN5HCdkBH3eACp1TCtCGfPni2/VL00oYkqnBd27tzZeGUdTCtCrvu0bt3aeKXRvJgpU6bInTZWW6owpQg5tKhbty4mTZpk5Gg0L4bzQXpXnT592sixBqYUIbcrcWmCO6g1mqjCqUuFChWwfv16I8camFKEytKlD/jUvCyMRWs144wpRbht2zaULVsWwcHBRo5GEzV4wOjQoUONV9bAlCJcsGCBHI56yiGRmpiDfsZWc/AwpQh/+uknGchHo3lZfH19pdO/lTClCHv37o127doZrzSaqMNDRblMYSVMKcK2bdti4MCBxiuz8QRXzhzE5vWB2LB5J85cse6ObjuyYsUKadRjXCKrYEoRMsz94MGDjVcmIjQEa8d3QumsKRArViyR4iHb2/Ux4fcTsOfJedZj3bp1chM4T+2yCqYUIcf05rNwPca+WV8jYwKK79kUP0tVzNhjPe99O8IwFxShlU5tNp0IGdipefPmGDFihJFjDp7cP43ePq//R4BPU1xU7zkf1tzXbS+2bt0qF+yttKXJlCLkGXTDhw83cszBo+sb0DhHoggE+DQV/mgodFhi97NlyxYpQis5/ptyOMrzyYcMGWK8MgdP7h1D13KpIxRgrFhxUKXLDDxvALRjxw74+/trBwQnQ5c1DketFALRlCLkjvpBgwYZr8zCI/zp9wVSRyTC9KUxflPkh9SsXbsWWbJkQdy4ceV2m8ePtRnHWfC7pgitFBLFlCLknrCePXsar0zEgyDMHNAUub2SGgKMDa/cFTFw1nZE5ttz5MgR5M2bN0ywzZo1055AToTeVgwGbKUDZE0pQp4/SOOMOXmI49tXY9b0KZg+eyG2H4/8zPzLly/L6ABKgN7e3jJigMZ5jBs3Do0bNzZeWQNTilBtzrQy7O14pLcSYJo0aeTJUhrnQicPq3lbmVKEPHuOXg9WDW3BoVCfPn3CBJggQQL4+fkZVzXOhNEYrHZcmilFuG/fPrlD+uTJk0aOteAhJUmSJAkTIb36Y3SO8uQfXDt3DPsOHMKZ4Igbqif3Q3Dy2CHsP3gCIfdDjVz706BBAzkktRKmFCHFx3CH3FdoNWidS5UqVZgAOT958OCBcTWGePIYd85vRvd6JeBd/GOs/c+qRyiW9Hsf2fJXxJAFB/B3qGdYY0NDQ6VRhseqWwlTivDq1asy0lpAQICRYw0OHDggjS9KgFw0pnHGOdzDjK/fQ+JY8dBk5GYhu395dGElmhZOjthvVkWANQcTr8S5c+dQpkwZ7Nmzx8ixBi4Q4SOc3xOIX/xGwXfoUPgO8cWwYSMwbtpCHAiOuIegB/xnn31mqfPpL1y4IIfQSoC5cuXCwYMHjavO4A6WjvJFm/dzI3PZz/HnVSNbiHP9xB/RsUlpZC3VCEutf6R7lOEOCo6geJyelXCBCB/j5sVDGPFFKcSPkxsD5wdiQ+A8dKpdHNlLNMCMHRF/YdzYyyOyrbCmxmjhjpbQtGnTYuXKlcZVZ3ETC8eMxdzfhsHHOwdaTX7a+j85GwjfwWMw27cV8peqi0XWCjwWLehlxf8Dh6VWwmXD0XUjmiB9mspYbvjV/n3YHwXixkKhT0cjIkcuzq18fHxkD2N2uAlZCTBevHiYOHGiccWZ3MTc4T/hjyMHMbNLeWQq3w3n/3mIXb/9hFEzt+FIQFfkKlLbY0RIL6SmTZuacwvcC3CZCNcOa4KM6SpjcbCx2fLeGlRNHgc56n6Pc09znkEN7zZv3mzkmBMKLn78+GEi5NKEa7iBub5Dsfp0CG7snYLSWXLi64kBGCcq4Ybgx7gyrw2yF/YcEfIYPTbazh+BxDwuFGFTeKUtg+mHr+LmrWtYMbgR0qfLh37zDz1jVFDQpF+/fn2MHj3ayDEfnIOkTJkyTICM9OU6n8W7CBg5EiuPcWgRgtGfFEKCdAXRcfRGMQsHgua0QY6idbE8SL7Z9tCSTkPYqVOnjBzr4DIR/j7yE3gl98ZXA/qjcflcyF7mI8zcclpWmMig98Onn35qvDIXdD9ztITyWC62xq7hCe5c3om+TRph4Oz1uCF0f3HFQBTJ/w7mnnyE0NuXsaxnRcRKngeDV5zBvVDr+FG+KlwbrFOnjuXmg8Slw9E3MryDpWfP4tcOZZEyS1UsOPF8owuHom+//TaCgszVnFNsjIuqBEgxOtcSGp7HuHpsIyYOHwK/BesRxD1UoRewZctB0N587/JxLJ00BL37fo9flv2FkIf2XiekNZ2jJkZasyKunRO+XhlLxOjpye3d+LLk68hcpScOPycUCL/c6tWry314ZoEL71yAVwKkJZRGJI37YMT2kiVLurghjDlcJsKNoz6GV5rKWBry9PWVzWNQME1yVO+zAM+bRf34449o2LChKbam8Bl4WpQSYMKECTFt2jTjqsZdsAdkT2hVXCDCx7h4IBDd3+f8KTW+mrwWZ66x+3uE9SMaIWmclHiv02is3XkmQjFy7lWqVClTHBbKeQeXICjA2LFjY8CAAcYVjbvgHJDeVa5ZFnIOLhHhtdN7EbhiERYuXIg1m/ch+JbhKRN6HVuXzcOv85Zh57HgCDfGcvjHCffIkSONHPewfPny/1hCrRRWz64wsBOHomfOWNc1yGXD0ejw888/o2rVqtIzxR1wV0eOHDnCBEhLKP1bNe6nW7duMlqBGaYrr4olRHjx4kVpJWVP6moYmKl06dJhAqRP6NGjR42rGnfCw0CLFi2K1atXGznWxBIiJAx5Ubt2bZeuAzFiF41CSoDp06fHH3/8YVzVuBuuI9erV89SQZ0iwjIi5Fph8eLFXdbq0ReRQx0lQO6O15ZQ88C1Ws4FlyxZYuRYF8uIkPTt21furHBFyEBaQrkEoUSoLaHmgssStIpa0UMmPJYSIXfccw7AQz+cCX1CU6f+N9AvXedifHe85pWhUYzLVvPnzzdyrI2lREi4bciZc8Pdu3fLQL1KgNwkGhJieBhoTAEDOdGTyl3W8pjGciLk3JCtoDNc2VTZSoB58uTRllCTwUYyf/78CAwMNHKsj+VESGbNmiWHpefPx9wRLAyvyPmmEmCGDBmcPuzVvByMskBrdfv27S29LhgeS4qQhhmead+mTRsjJ/p07do1TIB0TdOWUPMxY8YM2fiabVdNdLGkCMn+/fvlsCQmdjCMHTtW+oIqEVoteKwnoIwxjM5uNywrQsLAPgxxF53oWosXL0by5MnDBMhTgvWBLeaDJ3Vxp4QdliTCY2kR0lOibt268oz7V2H79u3PWEJpcbt2LfIDXjTugRHNCxYsaNn9gi/C0iIkx48fR+HChTF+/HgjJ2owkBT9UZUAeXwZN4dqzAV3SdBf12pRtV8Gy4uQLFu2TP6johqZ7c6dO3JoowSYLl06bNiwwbiqMQt0nmfEPbvP0W0hQsId+Jy4RyVOKU/LVQJkuMKZM2caVzRmglHY7eCg/SJsI0J1HiBP5bl7966R+1+4OVgJkMdX//DDD8YVjZngDolixYrJ7Up2xzYiJBy+0M2sRYsWEfp6cj9iihQpwkTYsmVLvTvehPAIBHor7dixw8ixN7YSIaEXDcMRdujQwch5Cv+hmTNnDhMgd+rfvHnTuKoxC5MmTZLzezu5pb0I24mQHDlyRHpW9OzZU75mD8m9Z0qA+fLlk1ZVjbmYPXs2cubMKdduPQlbipDQo6ZEiRJyDyLniUqAGTNmxJYtW4x3aczC0qVLkTt3bilET8O2IiQ7d+58JkIaf9eWUPNBn1DOATkU9URsLUL6hDIshRKh9gk1HyNGjJAC5M4YT8W2IqQl1PHseC8vL2k1dd2hLZrnwSMOevXqJZ3wPT14li1FSJ9Qzv2UALkTn7FDufhbqVIleba8xn3QY4nLQ5yz8//i6dhOhGfPnpWWUSVA+pUyNg3h2iG9ZQoVKmSLKF1WhMcZMEBTtWrVLHmWoDOwlQgZC6ZWrVphAozMEkpnb1ri+vXrJ2OLalwDjWIcfrZr1w43bhjnpmvsI0LutmfYAyXAJEmSYM6cOcbV/8KTXRnOnq2yHhI5FzaO/N9QgLSEap7FNiIcNmxYmAC5Sz4qB0YyrkzHjh1RoEABW+7YNgObNm1C+fLl5bzcrvsBo4stRDhv3jzZ8ykRMvbMywQI5gJxkSJF0LRpU+zZs8fI1USHy5cvy/CU9E769ttvtY/uc7C8CDnn4/KDEiDnhLdv3zauRp0TJ06gVatWcgc3K42es7wabPymT58uD9GpWbMmNm7caFzRRIalRcioW46749mbUUzRYc2aNdJyx82k7GG5nqWJGlwa4mZpLj34+fnZJjivs7G0CGlcUQLkiUkMhRATcCljzJgxcj8b/U6tfvSWs6GfbufOneXc+uuvv5ZH2WmijqVFSMNKnz595LBn1apVRm7MwfVFnlHPdUcGBuZpva44jMYqMBo2lxvYWHE+HdXwIppnsYVh5nk76WMCipG7MTjM4pwzICBAen14Iox8zXl48+bNZePEEJF8baeI2K7GFiJ0FRxm8bBSzkO5KXj06NFy76InQGsnF9s//PBDKT72gOwJNdFHi/AVoBM4z9Fnr8jNwjw6jUYcDo/tBAPtrl+/Xrr60VBFv1ue08g5oCbm0CKMBrT+0SLI9bCKFSvKRWme7stdAVY9L+H69evYtWuXdHZgMGRGsGNwZZ7ZqAMjOwctwhiCc0Run+Icib0GXeKaNWuGCRMmSCuumRer6VTN/XyMy8PlGQ63aRXmMoPe+uV8tAidAM/GYM/BRX+G6acoOYeki9zEiRNlT8m4N+4wZjC4FYNe0YeTxqY6derI8zxq1Kghe3H626pdJxrXoEXoZLjmSOMN54xcS2MPw2ErhUnncR50wsDFDPPOYSAPJeV2LBpCOMeMauBbOhWwN+bpRYw4x0BWdEyn88GoUaPkvI6BdPm5FB19OfnZbBToqqcjz7kPLUIXwyDFrPC0LHIIyJAbNOxwGEhxUCSMncq1T3qfNGnSREYE4C4EipjnKPbo0UP2Wl26dJG9K93tGPiYB2jSWMRet0KFCrI8Hx8fucbJe3i6MR2q2VPrM/jNgxahSaAlkksgPJSG6248X4NDRnrucFjLUBBKeOzV+JOvKa7+/fvLWC1Tp06VPSrP1WAveO7cOaevoWqijxahRuNmtAg1GjejRajRuBktQo3GzWgRajRuRotQo3EzWoQajVsB/g+9OyBxhaK9NwAAAABJRU5ErkJggg==)
A uniform disc of mass M and radius R is supported vertically by a pivot at its centre as shown. A small dense object of mass M is attached to the rim and raised to the highest point above the centre. The unstable system is then released. The angular speed of the system when the attached object passes directly beneath the pivot is
![](data:image/png;base64,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)
physics-General
physics-
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
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)
A bar of mass M & length L is in pure translatory motion with its centre of mass velocity V. It collides with and sticks to a second identical bar which is initially at rest. (Assume that it becomes one composite bar of length 2 L ). The angular velocity of the composite bar will be.
![](data:image/png;base64,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)
physics-General
physics-
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,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)
A small particle of mass m and its restraining cord are spinning with an angular velocity
on the horizontal surface of a smooth disc as shown. The force F is slightly relaxed, r increases and
changes.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQEAAACJCAYAAAAseI38AAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABpFSURBVHhe7Z0JuE5V28dNCUX66Cp8hpdX0xelMqXp7Wv0Jg0qChVJo6JRGjWg0kSiVKKZQtJkqogyJKXhFA3IlDJmiON+92+dfZ93eWzVCdd1nr3u33Wt63n22nuvvdZ61v1f415PETEMI2hMBAwjcEwEDCNwTASMLfh99TJZuHSFbJaNsmThQtkQ+xvpxUTAyCP3Vxnar4fc1ftJ+Wzectm4ab3MHjtYLr/iJvng2xXxRUYaMREwRDYulQc6/ltOvvhembtytbzRp7v0GflJJAxr5frj/in/6vSk/B5faqQPE4HgyZVxj7SXSrX/Xz5ZGR3+OFr23aO83PjyF+5sz9Nry/+1uFvWuCMjjZgIBE7uitly2gF7yL9vGeWOv3i+mxxy9Dny1aroYO3nckqtinJW95GRVBhpxUQgcJZMe0b+uUcVeXxmXl3/Vr+7pe+ome77V0O7SaWqh8nob6wdkGZMBAJn2ecvSt29a8uA6fNkQc7HclvHy2Xw5ByZ/82H0q7pv+SmpybGVxppxUQgEH7//Xe55ZZb5Kmnnop9YjYtl+H9uku3nn1l9IRpMufrmTJkQB954IEH5OV381oERroxEQiEefPmyS677CKNGzeWTZs2xb7/Jdfz27xhray3QYBgMBEIhO+++07Kly8vxx57rGzcuDH2/S+bN2+Wzblm+SFiIhAIP/zwg+y5555y3HHHSW6GsY8cOVKOPvpo6datW+xjhISJQCAsWbIkXwSUOXPmyMUXXyzFihWTIkWKSIcOHeIzRkiYCKSUDRs2yOTJk6V///5yxx13SMuWLZ2hIwQXXXSRXH755VK1alXnp65v375uANEICxOBlLFmzRrp3bu37LffflsYOI4xgd12220rf3UVKlSQGjVqyMsvvxyHZoSAiUDK6Nq1qzPoihUryoUXXigDBgyQESNGyKRJk2TmzJkyY8YMadq06VYCoI6WAmMERjiYCKQIRvhPPfVUZ8ynnXaajBs3LnEmAAYOHCjVq1ffQgCKFi0qgwYNiq8wQsFEIGVMnDhR6tSpk2/Y9Pvr1avnxIGWAeMBrVu3dsflypXbQgRq1qwpq1bx0oAREiYCKWTp0qVuZSBGf+CBB0rZsmW3MHZ19P9PPvlk6dixoxsrOPTQQ+MQjJAwEUg5q1evdtOD7733nuy+++5y+OGHy6xZs2T+/PmybNmy/NmA77//XhYsWOC+G2FhIhAIixYtcrV/w4YNYx/DyMNEIBCYOuzevbs888wzsU/6cEufI2cUDBMBI1UwHnLzzTe7AVLjr2EiEAg//fSTnHnmmYlTgLxLsG7dulTUop9++qnr9rAc2vhrmAgEwuzZs51xIAQ+c+fOde8MMG34yy+/xL47h8wXl7aHb7/91nVv3n333dgnDwY9S5QoIRdccEHsY/wZJgKB8NVXX0mpUqXk3HPPdcfr16+Xxx57zE0TIg6HHHKIm0nYkfD+wvLly90bjLystCNF4J133nHxLlOmjFx11VXuVWlA7Ng3gfUQxl/DRCAQEAHWApx//vny4YcfyoknnuiMSN39998fX7njYMUiKxfZ0eiRRx6JfXcMdF14I1LjX7t2bXnhhRdcd2DXXXc1ESgAJgKB8OWXX7r3CUqXLu3WC/gCwHLhBg0aOKNi05HtcUceeaS0aNHCTUkiPExJYpi0CnJyctyeBVdffbV06dJlu9z111/vwibumg5eiWYdBH6XXHJJnHLjzzARCIRvvvnGLQs+4IAD3EtCvggUL17cdQfq168vhx122N92rDgknFatWrmFR7iTTjrJbW0Go0ePdqsXqanpmmyPQ8xY9uyLgDr8Lr30UvdM488xEQgEXiT6+uuvZcWKFW76jFrUNxy6A1xDjb09jrEGhZbAUUcd5QQI2Nvw119/dQOQfG6PY6wBQ/fTgAj16NHDdXvatWvnnmn8OSYCgYABMk24du1ad4wh0TRnYA0DOuKII7Yw4B3BlClTpH379vL+++/HPjsOljzXqlXLxZ3ZAN5/YI0AA5A2MFgwTAQCAeOoUqWKdO7cOfbJgym2Jk2aOBFYvHhx7Ltj0NmAHTkroLz11ltOAPbff/8tNkFhitBEoGCYCAQCA4MlS5aUM844I/bJG2EHXh/++eefs2qxEPFl8xMdb1AYhGRMoE2bNrGP8WeYCAQC/XMG084555zYJ52wToCBQ2YgFHuf4I8xEQgEFYGzzz479kknv/32m7z99ttugRIDkAwgGn+MiUAgfPHFF24q0O8OpA2t8ZnluO222+SYY45xax8eeuihbW6zZpgIBAMzAyzmYalwmiGdTA+yaAnBY8Bzr732couLbDv1ZEwEAoER+hBqQ/5IlSXR1157rZx33nlu+7S6deu6hUUsVjK2xkQgEHhVmA1Fpk2bFvukD9ZAsGT5uuuucwODiAArFllKzH8u8PKUtQa2xkQgED777DO3ZJc/JaFLgCCwGWlaHOm58847neHfe++9cuWVV+aLAEuaK1eu7LZYt30Ut8ZEIBBGjRqVv7wWxzQaK+0YLNTPpHX42eKIO+8k8Ocr99xzzxYiQEuArdd5cWro0KFxjhiKiUBKodnLdBlNZBYDff755+7/BzGYtm3byvPPP+/6yK+//roTCFbgjRkzRsaOHZu1jtekb7/9drfZSKYI6B+tcN6HpdLkEVOJLK1mWnFnrHAszJgIpBBGyNlogxrx0UcfdX1h/oPgpZdecq/bsusOi4b4o9Jnn31WHnzwQVeD8gJQNsPegqTjj0SAcz5PP/20G0xkz4PBgwe7z2HDhsVnw8BEIGWsXLlS7rrrLnn44YfdbjsvvviiNG/e3BXuN9980xkCA2dMo1FzsoiI9/wRDMSAAcRshXTxUlRBWgK9evVy6UYMOffqq6/KDTfcEJ8NAxOBFKDNV14Suummm1xBBroDDJLxxyN9+vTJ35KLhTTUgE888YTrFij43X333e4NvWzkxhtvdEKACGaKQLVq1dyLRYijDwuJSDd5dt9997k8Ig8hlOXGJgIpYfr06W5BjP/aLoZPv59/IOLvyunza23IvxVj7Bg9240pw4cPdzUhXYpsg9qcbk/SwCBvUO6zzz5ulkRBPMmXfv36uXsRgVdeecWJAGMFJgJG1sDgHrUgm4Yo7O9HoQYMmnnzJ598Mn9MgOk0oMtAXxqhUD744AO32OaTTz6JfbID3hdo1qyZG+tgTMQXAVYNsnrQ/8NVRGDhwoUuf9RxzDRito+PFAQTgSyGQkxTliY/r9Yq7O9Hbaav2bLZxvHHHy+33nqrm0bDUNiVRxfOUPsxgOhDjUkYO2NDkJ0JA4O8RoyIsc2ZigCbp6R9yfTfpVCIAAWOwjxkyBDXR33uuedc84xPdfhz3vfDscMs/pnnuJ7RXg1H7+fPN/QZ6rgu088PT8Pyz+NH2HofnyxY0fv0HuLHpz5Dj7mG+9WfY+7V7/hr+LjM9A0cOND1fSnYfq2FMLBVGH1bhTSzOSddA7oDtAIYFBwxYoQ7z3Linj17uhaADzUjtSr95qR807j5+UA8iTvpxE/Tqun2/f3vfPrf/WcQPteqn4bpX4cfm4swJnDwwQe7VgBicMopp7jxgEqVKrl8YYYkMyw/HN/fvy7zXGYc/Tjp+R29hfvOolCIAG+4USAZvWbOmp1i6c8yd03B5dVQajGavOqH43oGdOgHMq3DsZ7jHvrI1AzcwzGFn74ix1zLJ81G9qVTP354Cg+1o17Tt29ft02Wfx9xYcRd/Vi1xh94EH+e1alTJ1foOGZeHuPQdDAwxzHPIf7s7oOR0lcnPK7jHkatOcYASSPfSSe75pAu4gh80hQG0o7RKgwWYvCkkVodEWAcgLhfccUV+d2AH3/80YWJ4QPdBMYHmC0gHeQbBkbcSC9GRmHnmK4Go+zEj40+mHlg0JFjpt9odZBGame9TsPEn/iQn4TFfdzPM3D40SIhz7gPhyjwD0OvvfZa/u+BAZJHb7zxhhODpk2bun0U69SpI2eddZb7HShj3Ee8NXzymfzlu5YdjR+/Id/VH0f6SDtx0Hu4BhElP4kvceCcbuVW2Cl03QEWbVBQMtd4M5DFnnWZML3FwE4SCAmbTChMl/nNWxaHMIjEn3UqhOcbEWAM/LA+FBL+zluhFqVwKTTRqQn4hx+/qU3NzcabLN7p379/7Jvnz7OB2pz7NV707xEnwEh5toKxIm5sIEp8GNSjXwvkIeMCxB2DY2ScEXL2FKAVgVHgx/OA1gNGS8uArcYQJe1mkA4/XxhfYDASpk6d6lomCqvyMDpghoLBN+LC74fBAekgjYCAIXjAb8IUnz8oRyWR2V0hDzKXACN0dIWAPKB1iZH7sx3kOfFV+M2S/reQ+xGnJLgns5tEPpHObHxJq9CJAAUeg/chgzFW/YF9MA5qhEyo2VBnNSSazBiLH8bkyZO3+lOMxx9/3MVBoVDSJPa3scJYKXD+xpwUUm1O85KOGgzCo3vgEQYFnxoCo1dRIzyMkmcBtaMaFcbDOebzgWamn14MjloQCNsvnJyjxmLtADUjcWaLMRYK0doiHhi9dh0wPIyLgUYgbyZMmOC+g58PGA4iC/w+KkSAyCHk2k0hb5iBQFgwLJ6rAoW4kG7fgBH1SZMmue9AuAiDb8y0fmja+5DPmcuCeZ62boD0+JUG8Ur6YxRtASFAmSAiKlqggkUaEPdso9CIgGYkapr5phs/FIU1E4wQf/bPy0TnxhV+TH4kH35832gonBQ2v4ZhvCJT4TE6nYsHdu7FALWQ0jVQQ6Kg66g9TUWMmxYChk0tCXQNaGYqdD+0duL5WjtTY2Nc7KMH5BlCN3/+fFer++mlMFKTk0cIDi2E8ePH53cHGDRDoIgz3QDCAAYRWXCDQZKHfg2PoND8Bc6TVwgM8aCGVcHgmPTpVuO+oZEfM2fOdN/JJ00332lWA5/E2YfwEUcFkUd4/PEQ8or88EEY/BWA5D1dIe2vI0xUMKQ7EwQ3afUgMwykT/NMIS3kabZRqFoCNMH4QTK3hGLATQufD81ICrrWoD70LX0DpwD7Nai2Lvwf/6OPPnI1uDaPKcwYqG/wugBH++BAsxjjBISE89Q+PIP4qcARNoLAfD1pAuJOgdKuhd6jLRgKsRYsnslz9ByGQG1FKwHD1ZqYOBIGwofTuXPW1yMC1OgIAX1eCjItH79moxYmXPIGQ9MWz8cff+wEkfSQRxi2tmYIgzxXqKW1ptaanHCowbVlRI2q4sBvpYaPCGPMCIyCAPjdJ/KNOM+YMSP2yTNw8l67Q8A0J2nR3wBoCWirDX/SRKswE+71u0s+tBj9wVdg/IW8zTYKlQiQqRhdJhRYvymoULOi1pnQ1NRaSqE21T43UDvxQ/pgmISpYEyEQ02vYMQUKh9aBhg2UANr/xXD0KY6tQfpoEDxXG3tEJ7f36W29mtfnqVNcGpmakyFsQpqKsTFn9PnGkSPWhIxoGblGaQNEaAm5BqEVdPCp983pktGa4ZPzTcdr1Hh5H41dJ5F+hBBQLAwSIW8JXxe0NHamrwgfuQzwkZLTQWO+PjrHhAS7vOXNfP8zN+fsQo/Hdrl8bsEGLz/2/Pb6e+UCb+/v7ZAIU8yywHlDkHJtteVC4UIULjIVBat0KylVkRVKUgUXEalOc8gGP44akFG1Kml9Xq9B+NgtJm/r+YcxnPNNde4QkUYOGpfDIXzOParv+yyy1xTlfOEQ/OOZjTPou+KHwWRGonvXEeTl0E3Ch7XURMQLobLqDa1OLUttSQFhFYDo8gMWHI/BkyNxr0c8zwMm2Pizf8EkC7iSNiMgfBs8kP/149aXo0DEWIGAgNjYIy8wGiJN0aDCJDPdDkwXIycPOYaugUqtqSXdBEfamjig+OZGAxxoPnPiD95QHoZwSe9nCOvmZ2h9cE5xJ1WhYaLIeJPmrgHI+V3Rnh4DqJFHAlL857fm7iSF+QVrQfyh5aQ/maIG2LEMY5nkF6eoffReiDfaMXgR4VAnCgvnPfLEiKgea7+XMPvRxikQ88Rb55NS4Nws2WQsFCIAM1PCjKGS2FFuek7YjQUEmou9VPHOYyM2sY/hz+FEUPgO+f4IbkWY+MaFJxnUfNwnmPC4Rru4Rr8CYfna/ic4z59JvcRX+6jhsSgMRrC5TtGRaGgScl3hEevJy6EQQEl7YRNeJzjfo55NjWlPotreTbneB4GyHQaxkN4GDWGRoFk3IBnUzshQjyf7hDv3TPdSViAAPOdbggCjFjRRNYpxA4dOjjD55k8g/iQLxon8oO4cMyz/XznPtLAfVxDHPjEn7zgOu7hmPziXo7xJ+5cTzj+76q/B8/mk/wmT/WYcEkP13MfzyYtfj7yLPKZZ+CH41jD4T4tA1zD/Rqefw5/4st3/LiG+JEenqvds8JOoRAB+ncUVkA9Kcwc88k5CiXHvuMccF6vV39qQb1HwwD/OvDvVdXW8344eg2fkPlM0HiDnve/Ew7hZT5H/TU80LC41087aHhcw3ccNRiFj6krRsfpG1MQqbGAWpWWEN0CWgIUeJYOaxeCbgsFmXggQPT9MSbEg/A1Pn46/PjyyTH+/jmu1fjyqdeChunfk3k9xxpW5nn8NCz97t/n+3HsxwsHGgc91nO+y0yT78CPj/8sjvmeDRSqMQHj70E/m511qWWBZrSOatPNYa6c1hCDa4gA32n+0pLQQT9qLsSA/iwCQg1L68BIPyYCWYzWNBguO+xSc2stTk1Ec5TvjAUwfagDgzS7GXxELHTmgakymrd0DxgL4V0DHaQz0o2JQBajTU9qdpbmMspOf5iBKmCknO4Bg370Wf3ZAUbHmUqjG6GrKmkJ0F9GQFhq7E+xGunFRCDLoTnPLAD9fAxbpyqZg8fAMWhGrX0RoLlPy4A+MQtsEAVqfUSFeXumahnZ17CMdGMikMVod4AmPK/M0rwHBgYZDdclrAwQJomANveZw9d5clYCMirPdCljDUb6MRFIAczTn3766U4MgHUKuioPmINn6ksHBhkTYO6f0WygS8GsgC4KYs3DCSec4MTESD8mAlkOBoyBs1EI03yMCWDAtASY98bRtG/ZsqVbSMNbhPT3eZOQsQSd4+cVW/69BzFgLQJh+C/xGOnFRCDLQQRYnUdtj2NFIu8LMOjHajkc51kJyRJbFgvRHeClK1oQrDHgkxVutABYZMQKPc7rOgMj3ZgIJECzmFdtW7ZqKee3bl2oXes2baRd+/ZyUbt2brOR9lGNjuM7fiwKopZnaS37CtAdYKkw3YVGjRpJg4YN813jI46QhrFfo8aNpX6DBnJIvXpS79BDC7GL4xfFU1/KMgqGiUACTJNhLGlyzB7oq8SMGfBmYeY12e46duwY/4JGQTARSKBH1I+mUFUsUlSqFikulbPUVYlcxSLFXFp4+YYXfviOCFwSGQzfqxQtJtWKFZEaUTch21y1oiWkZpFdpFLR4i4tvOtgFBwTgQR63nefK1QUrlqREdWIxABX3XNJfts65x9v69y2/LZ1zj/e1rl/RK5SlA7SwktGSSLwv1H6akaf1bPQVYtErmaREk7wnAhceWX8CxoFwUQgARWBvYoVl+pRTVk1+p6Nrlrk9o7cViIwKBKBS/NEoFIkAv+IPpPuL+yuSix2e0etAhOBv4+JQAIqAntHLYGakZEk1ULZ4GpEbp/I/ZEIVMnilgBCQNwrFc1Lo4nA38NEIAEVgX3yuwN5BpVtjho+sTvgiQDdgVrRZ9L9hd3R0iHulU0EtgsTgQTu7dHDFapykWNwsEL0ma2ONJAWdsHR2QGm0phC5HvJyJWJXNnIcW02ud0iR7xLR460MM5hFBwTgQRYVFOiRN5gU1ocuxfpsmHWCbCDEP/PV7ZcOSm7xx5Svnz2uT2jeP8PcY/SUKFCBbfy0Sg4JgIJ/LZ6jYwcPlwGPfusDIkE4bksdoOHDHE7/LJZKvsEIAL699ysLGSH5WnTp8vULHTTp0WO71OnupWOusmpUTBMBAKCPQZ9ETAMMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYAwETCSMBEICBMBIwkTgYDgn4gRgd69e8c+hmEiEBSTJk2SJk2ayLBhw2IfwzARCI4xY8ZI69atZf78+bGPETomAoHRqVMn1yVADAwDTAQCo3Pnzk4Exo4dG/sYoWMiEBhdunRxIjBu3LjYxwgdE4HAMBEwMjERCAwTASMTE4HAMBEwMjERCAwTASMTE4HAMBEwMjERCAwVgfHjx8c+RuiYCATA4sWL81cIdu3a1YnAlClTJDc3V+bOnSs5OTnuuxEmJgIpZ+nSpXLQQQdJmTJlpFWrVu7dAUSgbdu20rx5cyldurSUKlVKFi1aFN9hhIaJQMpZt26dtGjRwhn+tlyzZs3cdUaYmAgEAK2B+vXrb1MAVq1aFV9phIiJQCDMmjVLKleuvIUANGrUyLoBholASIwaNUpKlizpBGDfffeVOXPmxGeMkDERCIxevXpJ3bp1ZeLEibGPETomAgGyYuXK+JthmAgEw7qVv8iCBQvcmoGlixbJ0uVr4jNG6JgIBMIvnw2XFiefKg++NkHefOlxeWLo+7Le1gcZESYCofDrNLn47DYyfnH0ff0yWbx8rWwyETAiTARCYfkM6XDaqXJH30HS75EB8qX1BowYE4FQWDFDOrZoJc9NzpGc2bNlydrY3wgeE4FCwWbZsDF3pzbPN8wbI82PPUmG5tjyYGNLTAQKBbmyZMV6WbUhPtwJ/PzlBOnerZu8Pm1e7FMwNsefRvowETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjMAxETCMwDERMIzAMREwjKAR+Q/261TQMlwZXgAAAABJRU5ErkJggg==)
physics-General
physics-
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
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)
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate abut its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOMAAAByCAYAAAChtGaqAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABTBSURBVHhe7Z0HeBTV3saX3lKAEAiEjiKRi4QOH13F4FV6/wQRlaryXfTjYjC0KEThShGFUFQwgHSlSUC6CEhvgdAEE0gILZAYEgLhvfsedtZN2CRqdieb3f/vec4DmTk7O7Mz75z2LwYIguAQiBj/Jg8ePMD9+/fVvxmLtl0Q/goiRivcu3cPt27dQkxMDH799VecOnUKhw8fxk8//YTVq1dj9uzZ+OSTT/Dxxx9nWiZPnozQ0FCsXLkS27dvx4EDB3D8+HGcPXsWUVFRuHbtGhITE03fKAgiRsXNmzeV4Ci2JUuWYMyYMejfvz9efPFF1KtXD+XLl0e+fPlgMBhyVDw8PFCzZk20atUKPXv2xDvvvIOZM2ciPDxciZ0iTUtLM52V4Gq4rBjZ6u3cuROzZs3Cq6++ijp16lgVEEuBAgXg6emJihUr4qmnnkKDBg3QvHlztGzZEi1atHiscDv3s56fnx+qVKmCMmXKoFixYlaPz+Lj44OAgABMmDABW7ZswZUrV0xnKrgKLiVGdg03b96supGdOnVCqVKl0gnC3d0dTz/9NNq1a4dXXnkFQ4cOVa3kjBkzsGjRImzcuBG//PILLly4oI5148aNTEtcXBzOnz+PgwcP4scff8SKFSswd+5chISE4L333sPrr7+Ozp07o3HjxqhQoUK68yhSpAg6duyIqVOnqi5uQkKC6QoEZ8bpxZiSkqK6n3ywu3fvDi8vr3QPPsXXp08fBAcHK8Ht3btXCU0PODY9ffo01q9fj88++wxDhgxBw4YN052fr6+varm/+OIL/Pzzz7h7967p04Kz4bRiPHHiBD7//HP07dsXTz75ZLoH/JlnnsHgwYPVBAvFR8E6CpzkmTdvHt544w3UqFEj3Xmzi8wXB1vXTZs2OdR5CznH6cTIbuSIESOstjCclGFXkV1HLj84MsnJydi9e7ea4OFkT8YWneNQbt+wYYPpE0Jex2nEyAeXYzxOmGgPrDb2YheQ+2/fvm2qnbdgt5ljR3ZV2dJzIkm7xkqVKqnr5myskLfJ82LkQ8oxVfXq1c0PaLly5TBy5Ejs2LHD6WYluQxz6NAhJUzLFw+7sG+99ZZq9YW8SZ4VIyczevfurbqf2gPJWUnOfvJhdYWJDk7+BAYGomTJkubfoFq1amq8eezYMVMtIa+Q58RIi5jhw4erdTntAaxcuTImTZqkFu45Q+lKcGzJLuq7776r1jK134RjyqCgIFy9etVUU3B08owYKbIFCxakmxnleIlrhlz3S01NNdV0TdgT4MuI3XNLUdavXx/fffed2MrmAfKEGKOjo9UkReHChdUDxm4Zx0dnzpyRhywDfGkdOXJEGS1oFj8lSpRQraRe66fC38PhxcixYbNmzcxvepqabd26VUSYDVy6WbVqFerWrWv+7dq3b499+/aZagiOhsOK8eHDh8oyReuW0jaUY0WamQl/nnPnzqn1Va2V5IQX11rv3LljqiE4Cg4rRnpPaDabXFf76quvTHuEvwpbyenTp6tJHa2VHDZsmHRbHQyHFCN9ADUh0uVo3bp1pj1CTqCXCj1DNEFyCSQ+Pt60V8htHE6M9O3jWhkfFi5q08hbsB3s5tMuVxMku/7i5OwYOJQYKbxatWqph+SJJ55QEzWC7eF4kS5c/J3pNP3RRx+Z9gi5icOIkVYzmoNv1apVsWbNGtMewR5wvNi1a1f1e3Op6IcffjDtEXILhxAjF6vpZMsHgyEu6Fco2B+u09Kmlb87f39aNwm5R66LkV7xXKDmA0E3IYbB+LtriKm3ohBxeC9+3rNX+SmmL/uw/+ARnDx3GXcc23tKV5YuXWo2pujVq5eYz+UiuSpGBl+i9wFdnfLnz6+MvHNiWxq3aQr6NK+JJ2pUQ+VKFdWSyB+lEipXqYYn/eqiaZsu+NeMdTgn0SzUi4/WORQjy8CBA1VkPEF/clWMbLHYLeVD0KFDhxwvRF9e9i80KGF8qHw7YOKsJVi7ZjWWL19uLCuwYsVyLFk4GxOHd8MzXsY6bpXRc+I6/CqGPCrGDmdVeR8KFiyogmIJ+pNrYoyNjVWhEPkAcAaVZm855crKkWhGoTUeh6M3TBszkpqAA4v/H/XYEjzzJhafcC0vj8y4fv06+vXrp+4H4wJxQk3Ql1wRIy1CJk6cqG580aJFMW3aNGX+llP+EOMYHMrCau7iphA0z2es93R/LDzi2t4eljAagre3txoyjB071rRV0ItcESO7p1qYRDoI2yqwkhJjGbZ4b2HNLxeUtwfL5ctXEHv1KqLPH8Xmr8eje/0yxpeAD9oHLsU5mcwx8/vvvyvvGN4XGphL66gvuouRcWgYs1TrntrSI/3Kyn+jRTmjGAu5wbu876OJG98K8CnjieJFCqNIcQ94+1ZD7aYvYfiM9Th3R6J3Z4ShSjR/SEY8d3U/UT3RXYzffPONutHsCk2ZMsW01TZQjM29jWKs/E+8H/IFvpw/D3NDZ+LjwIEIqOONQoYS8P/fEPz4q5h/ZQZnVxnKg5Y5XGoSu2D90FWMnC2l5znF2KZNG5tHyjaPGRt9gP1X0k+TJkftwKSuteBuyI9aHYOw4YKsa2RGRESE2QiDwb7E3UofdBUj/RM5dV6oUCG15GBrzGJsOBr7oh+fJU2J2obxAb7Ib3zInvznOGyLSTbtETLCLFrMMcJYQ7t27TJtFeyJrmJk0F2+bRnR2x75I/4QYyD2RlmfFLp1ahkG1mNAYA80eX0uTsbnfBbXGeHkTe3atdX9oiG5qwX6yg10EyNdd+ijyLEILT7sQfTioahlfHgMNYZj16XMWr1URG2fjIBKxnrGMWSjt7/BmWsypZoRTtxorlbPP/+8Slcn2BfdxMg0Z25ubsr0bdu2baattiUhIhxzJwUhaPZmRN3OSmC3EREeiqDRo/D+9BU4ESszhtZgrhIOK7j2yCBXgn3RTYwM+8AxCGfoaH0jOD50q9IiLjDRjmBfdBMjQzzwpjIhjYw/8gaRkZFo1KiRum806LeFlZSQObqJsUmTJuqm0ivA0TNACY/gS1Mz0GAAKwnPYV90ESNN0ui9z5vKFGfyhs070AqH961169bqPgr2Qxcx0gCZmaF4U2Xskbf49NNP1VifpoXstgr2QxcxMm0bZ+S4rOGMEa25DMB1ORo18MXjTDn458yZoyIBlC1bVoVHEeyHLmKk8bEmRmbapSe5VphvkMbjlqE26MVhWceysD7HLpZdXSZ94XZr9VmSkpJMNR9FKqd3Qlb1LSeYWJ/nZ60eC9OV02SMs8QeHh7KG6Vdu3bqBWStPk3L/sq18lwtr5XXktW5W6bC4+f4W2VWnzFTLa+V55XxWmmJI2LUB13ESHMqzROAU+UMw6gVRrmmvSoDFxM+EPQ0Z/JTxk+1rMsc96z/wgsvYP/+/ao+jQk4ucCMVNyfsT6PQzctLS0Au1rMOcHjWNbV6vPfUaNGqVRrhC1dvXr1rJ4L/y1durS6royFa6r8bstz4riZs8laV51hR/hd3Gft+Ex1xwgIR48eVfV5DQyxaO1atd+Ls9aMK0SYKo6/Fetb1tXqM0D06NGjzWLneTFCn3YuTK2g3Tf+BhcvXlT1BPugixgZhYz+cXzD0luDLaRWeKNpCPDBBx+ounwzd+7cWdXjPsu6Wn0+IFq4f3YPGzRoYLWuVig87YGmwQFbsKzqUzBapO3Q0FDlAG2tHguPk1XJWJfXOnXqVHVstnJt27bN8lrZo1i2bJmqzy6+v7+/1bpafYrp+PHjqj5fcFldK7+Xs9yamxSdvHl+lvVpR8yFf+6zbNEF26OLGAm7p2zx6EE+btw4c6EIeaPPnj1rqgns2bNH2UMyQJVlXa0+E7ewC0X4IG3cuFEdN+OxtW2LFy82P0jsJvJvHseyrlaf/7KLyVaLMFoaLVEyHnv8+PFqm2WGLMvCloWtHutpn+F30vjh0qVL6tiEvYYPP/zQ6rWy1WJOSu3FwGtdu3at+boy1ucxtB4G4efospbZtQYHB6shhAZN3mbMmKHMFbV6vGf0O2XuE8G+6CZGZ+XkyZMqyxO7jWzF2CVkbB+mKXAG2DWlwXi3bt1Ur0WwHyJGG8GxJWOQUoScdHEW2FIynRyHBjKBY19EjEKm0FKKrb7W9V69enW6mV3BtogYhUxhfCLNNpWTOVzCcaY1VEdDxChkCruonEnWWkaupZ4/f960V7A1IkbBKjRGoFG/JkQWmsWtWLFCuqp2QsQoWOXAgQPmNU1LMTKNnHhv2AcRo2AVetdwsd9SjCy0OBJLHPsgYhQeg0szQ4YMeUyILFzmCAsLk66qHRAx/g0epqUpi54HD9LgjI8k0y/4+flZFSNN6GjUYGmQLtgGEeOfJO1eImJO78ayWSEYPeItDB44EIMGv4N/T5iGJVuO4crtZDiL5SbtcbmUYU2MLPRNtTTpE2yDiDFbHuBWZDimDGiNGmXLwMe3Gvz8m6D1s23Rqml91KpeET7eXqjauBsmLD2Ia3k8vA9tdwcNGmQWHoMYu7u7Kxcq5v7ntuLFi2P27NmmTwi2QsSYJWmI2xuKvv9wR+HiFdDilXFYvuc8bt1NRnJKCpKT7+LmxYNYOWUwWlZ1Q4FCldF54kbE5uEQP/RqoehKlCiBgIAA7Ny5U3nRsLVkoVcIu6p0qZLAYrZFxJgF9+P2YEKbUjDkL4+XJ4Qjq2z3V3d9ioBKBWEoWhsj1l4yyjhvwmgFdEljNDgtcFiXLl3w7bffqv/HxMSoLMcMbCxLHLZFxJgZD+/ht++HoaKxW1am4VBsuGnanikp+GlsG3jmM46pXpqBc6l5c2pHcx2zhC3jokWLTH89ImO0BSHniBgz4/5t7Hi/oXGM5IY6AxbiumlzVtzdGYS6HgVRxLcXlsY5TzhKa2IUbI+IMTNSrmPVwBow5CuJRu+u/1MzpanHp6G1V2EUKh2A2Rdsk43ZERAx6oOIMTOMLePOQFPL+FoYsu2lGknaHog6HgVQuFIfrHKiZDoiRn0QMWbKA8RsGoWaxjGgZ90BWJVtepAkbHu/BdyNY8xKPebh0n3nGU+JGPVBxJgF9xNP4IsejITujiZDF+BYpgl87yFyzVi0LGuAwbMpgrfFOpVljohRH0SM2ZB49nu8F1BFCbL2y8MweeFGHDz9G+Ku30Bc9Fkc2rYCU0f2RH3vfDC4+2PgrD24lVfXNTJBxKgPIsY/we/Rv2DRh2+gRY0y8Cjpjao1a6Ouvz/q/uMpVC3vjTI+1dGsx0jM33zS6YRIRIz6IGL8s6Ql4HLkEezauBzzpoeoEIwTp8zE18t/wO7DpxF103lmTzMiYtQHEePfxNriuLMiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtkiYtQHEaOQLSJGfRAxCtmSczE+xL2kRCQlZRXOMg0piYn4PTnVaUJe/lVEjEK22KJljFoTjD6dOuKN/2zH7Yz+ZWkx2D5nOF56vh+mhUfCea18s0bEKGSLLcSYcGIW2pU2wFC+I8LOp4+CkHDyW/SvZtxXoQtC993Ks5H1coqIUcgW24wZE7BtdAuUKFQKzwbvQrJpKxCH7VM6ws1QCu2DN+C6q/ZRjYgYhWyx1QRO8vkwdKlYBCVrv4bvYh5tu3tuLd6uWwgGv35YcMxVO6iPEDEK2WIrMSItHj++3xTFilVEl5mnjRsSsD+0F0obPPHCmHWIc9X+qQkRo5AtNhOjkcTIBejsUwy+bYMQfmwnxjYrDEPNXvjyiKQKEDEK2WJLMSL1Bjb+uxm8fKqjTa9uqFnIC21HfZ9l6gRXQcQoZEu3bt2watUq0185Jz5iIXr4PspyVaBmD8w57NpjRQ0Ro2CV2NhYldefWaiaNGmCcePGITIy0jaZp5LjsP0/fdCyxQsY9MkGaRVNiBiFdDCF+LJly1TmKU9PT9V6sTB5KtPBjR49GqdOnTLVFmyJiFEww9TgISEhKm+/JkJrpWnTpjhx4oTpU4KtEDEKZjZs2IBSpUqZRVerVi306dMHAwYMUIlTmbFY29e1a1fJ629jRIyCgmPBUaNGmcXWoUMH7Nu3zxySMi4uDgsXLoSXl5faT9FGRESofYJtEDEKiqSkJJWRWBPjm2+++Vgy1IMHD6oc/9zPVOP8W7AdIkZBwRYwLCxMTdRQbJy8efnllxEUFITJkydj2LBh8PPzM+/nuDE+Pt70acEWiBgFMxRX3759za2jVgoUKJDu79KlS2PdunWmTwm2QsQopOPq1atqTdHb2zudALXy3HPPITw83KXSG+iFiFF4DE7mnDx5EkuXLlXCDAwMxNSpU7Fjxw5cvnzZVEuwNSJGIUsozJSUFGkJdUDEKAgOgohREBwEEaMgOAgiRkFwEESMrsyDJJzatAhhy7YiMi4Kh7aswtezpmHa5/OxLHw/LiUY66TF48yeDQibMxPTZ4RiyfpdiIgRm1R7IGJ0Ze5GI7RLeRT1fAovvdYdrZo0QqOmzVCvehkUKeqD596ehMnBI9C9VUM0atIMDWv7okhBT/j3mISfrqYPtyjkHBGjK3M3Fgv6VoLBkB/lGvfH/K0RiEtIRMzRb/F/z5ZTi/we/r0RsnofouMTcP38LnzcqRoK5fdC7wUXXDbyt70QMboyRjF+3bsc8rtVRb8vo00byTWsDw5AUYMbOn22C3dMW8lvc7rDx8MdzcfscdnI3/ZCxOjK3I3Blz3Lomg5fwRusWznrmLdR+3hZqiCwYsP4Y8R4kP8Nr83fDxLGsW4W8RoY0SMrowSow+K+TTAmO2ppo0kFmuNLWMJQ2UMCjuIJNNWivHSvF5KjC3G/ixitDEiRlfGQoxB20SMuY2I0ZUxinF+d28U9vbH6K3pxbhmfDvjmNEXb35zIL0Y5/aAt5s7/idIuqm2RsToyqiWsZxxzGi9ZSxuqGS1ZSzn4Sktox0QMabjITJEmtAR43eb/qcbD+8j/vJZRJ69iGtJlt9+H4nXoxB5+hxibyenS9GWGn8ZZ8+cwaXrd/U/X6fl0XMnYrTgQeI1xN1Kwj3dvYUeIuX2ddxIvCcPuAvyICEOV27ew38B1hxeXQbxL9kAAAAASUVORK5CYII=)
physics-General
physics-
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
![](data:image/png;base64,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)
A uniform 50 kg pole ABC is balanced in the vertical position. A 500 N horizontal force is suddenly applied at B as shown in fig. If the coefficient of kinetic friction between pole and surface is 0.3. The initial acceleration of point
is
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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 of mass m and length 1 is hinged at one of its end A as shown in fig. A force F is applied at a distance x from A. The acceleration of centre of mass (A) varies with x as
"![](data:image/png;base64,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)
A rod of mass m and length 1 is hinged at one of its end A as shown in fig. A force F is applied at a distance x from A. The acceleration of centre of mass (A) varies with x as
"![](data:image/png;base64,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)
physics-General
physics-
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](data:image/png;base64,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)
A uniform wheel of moment of inertia 1 as shown is pivoted on a horizontal axis through its centre so that its plane is vertical. A small mass m is stuck on the rim of the wheel as shown. The angular acceleration of the wheel when mass is at point A is
and when mass is at point B is
. Then
![](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 ![left parenthesis g equals 10 blank m divided by s to the power of 2 end exponent right parenthesis](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 ![left parenthesis g equals 10 blank m divided by s to the power of 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 uniform rod of mass m, length l 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
along 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 l 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
along 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-
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,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)
Moment of inertia of a triangle plane of mass M shown in the figure, about vertical axis AB is:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANEAAACiCAYAAADfjCiAAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABlmSURBVHhe7Z0JWFRVG8dHxTVzCVEEMTXLzCXc91xyX9LMyvUzK7VMLUrNtdxRc98xzV1zrdwtDZfczdIUUwRUwDRQEQlk8//Ne7hXh+GgwAzMvZf39zznwTlzMZuZ37znvuec95jAMIxNsEQMYyMsEcPYCEvEMDbCEjGMjbBEDGMjLBHD2AhLxDA2whIxmUgCAs+dwOHj53A/UekyICwRk2kkhB5Ai7L5kSufB+buD1F6jQdLxGQavnP6oXiRwihRtAhqdp2MKKXfaLBETOYQF4oPahdDxbe+xspJ3ZDjmQr46dJ95UljwRIxmcLNowvhbDLh0/WXkRiyE+VymdD2qx+VZ40FS8RkAnFY2q82TM71cTz8oflxNEa38YBT6TY4G5l0hZFgibIJFy5cwB9//KE8ylwSbhxG/WI50NhrjdIDXNs9CflNuTBkzVmlxziwRNmAuLg41K9fH3ny5MHEiRNx+/Zt5ZnM4cTyT2EyD+XqdB6ASRPGY/z4CRjn1ROFzH0erYfjdoJyoUFgibIBiYmJGDZsmPhgU6tSpQrWrl0r+u3Ow3AMaeGBHIXcUbt2bVTz9MSrr3qiRq06qFy2GEx5y2D5qTDlYmPAEmUTzp07hwIFCjwSiVr79u3x22+/KVfYh7unv4Or+e9uM+p7RN6PQuS9e7hnbvejohDgu1A8V2/AUsQr1xsBliib8PDhQzRr1iyZRNRIrIEDByIwMFC50hbiseqz12DK9Tw2/CXJICTewuBG5mhUtB4OBT9QOvUPS5SN+Pbbb1NIpDYPDw/MnDkT9++nPpdz584dXLlyBVevXk3WosxRhogJPoQaBUwo+trnCKOknIRjSz4S/72OE7bDKCuBWKJsxLFjx5AzZ84UAlm2WrVq4YcffhCRy5p33nlHRLP3338f7733nvhJQ0L6SfdXMeEB+GH9Rhy5cEP5jZQk3gvGjk0bsfOIH0vE6ItLly6hU6dOUnFkrWPHjvjzzz+V306CZNm+fbu4x4mIiBA/T58+jS5dujwxghkdligbsHnzZri6ukpleVKbNm2a8jck8emnn6ZIRNBwrk+fPiwRY1xIoGeffVYqidpo/ogko6Gal5cXFi1ahA0bNuDff/9V/pYkBg8ejIMHDyqPkqB7JBrasUSMISGBcuXKlUKacuXKoWXLlhgwYIAQ5vjx4wgPDxeTsk+CJZLDEhmUv/76S6SvK1asiM6dO+PDDz/EypUrcfToUVy/fl25Kn2wRHJYIoPyxRdfiKhjz/VyaZGIsnq3bt1CbGyseJwdYIkMSFhYGIoVK4Y2bdooPfYhLRL9888/eP7558XSorlz5yIgIED0GxmWyIBs3LhRRCH6aU/SIlFMTAzmzJmDSpUqiX8DJTU+/vhjIbZRYYkMyPz585EjRw4cOXJE6bEP6bknoiTF7t278fbbbwuZaBU5pcONCEtkQCjjRhLZe3FpRhMLS5cuFSKVLFkSe/bsUXqNA0tkQLQQiaw5cOAAXnzxRZEx3Llzp9JrDFgiA/L999+Lb/5NmzYpPfbBFomIy5cvo2zZsihRogRu3Eh9fZ3eYIkMCKWYCxUqhF69eik99sFWiQhae0eCjxgxInM2BToAlsig0KLQokWLiu0L9sIeEtH8Udu2bcVqcopMRoAlMiiZkea2h0TEqlWrxL+NopIRYIkMCt1zUCRq3bq10mM79pKIVlHkzp0bX375pdKjb1giAzNmzBjxjU/ZOntgL4lCQkJQsGBBsQDWCLBEBoa2bbdo0UKIRBk7W7GXRLSRj+6Jvv76a6VH37BEBof2BFWtWlVk66iAoy3YS6Lly5cLsY0y8coSZQPOnj0r1rBVqFBB1FnIKPaQKCEhAc2bNxf/nuDgYKVX37BEWcnDeNz59x8EXwtCwNVgRGdhJVD61qeV3RQBaP6IhlTpxR4SrV+/XvwbpkyZovToH5YoK0mMxnnfdWhf1R2enUcjLIvL6fr5+aF///5iOzh9kLt3745Tp04pzz4dWyWihIKbmxtefvllUeTEKOhOInrT6M3QLff90KFyMbw5bpfSkfVcvHhRCKHKRJGJ1rZFR0crV8ixRSJawV2nTh04OTnB19dX6TUGupOIMjpLlixRHumP8DNrUblkGSw+FaH0OI7z58+LNHO+fPmETLQHiJbj/P7773jwIGWF0oxKtG3bNrGCmwRat26d0mscdCfRuHHj0iURfVAWLFiA1atXKz2OZf+sbnCp+C6uaKiKLu0+pfJYDRo0EDJRq1mzJry9vZPVnhsyZEiKxIQqkVoF1ZL4+Hj4+PiIYinly5fHr7/+qjxjLHQn0fjx48X+FBk0zqYCHXTz2q9fP9SoUQMuLi7iQ2GvCUfbiMLI5uVQ7+PFDqv+GRkZKbYi0JBOFm0okzdhwgRUrlxZvG60pYKEotedNthRdVTL+glUJYjuswjKvNGw7ZdffsFXX32FatWqib+D5Lx27Zq4xojoUiKqWkP8999/YgkJ7eWn6pw05lbH+ZZt6tSp4nqHc2MvapTywOgNjjvo6u7duyLVTUM4qjP3ySefiHkbWgxqvaqaog4tzaF6CeprWbhwYXh6eooFrvSaUyUh2idEJYbr1q2brMYdXUdbxY2URJChO4koNUrrwWglMO1LoXG2+qbJGqV1aQhIQxP6hs2KRqLPmDEjxQrqC+uGo2SZ6tgT5NhTrihaqxFabUWKFBGTsnRCBH1JWafAz5w5I+Z3WrVqhddff10UI6HX39nZGXnz5hXFH0mivn37iqGzv7+/qLeQHdCdRCQDpWYHDRokvunoTbT8MFi35557DrNnz8aKFSvEqQhZ1WilMtWrfkws5vVrhPKNP0O40kNQinnhwoViiJpVjVZ2v/XWW9LXS220A5WkomVDVD6YogklHUgmgiIarYY4ceIE3n33XQQFBYn+7Iguh3OWSYLQ0FBs3boVo0ePFkXY6dvR+gMxdOhQ5WoHEuWPt6sURSfv5DfXdP8watQoaUTLrPbNN9+I18r6dbJutL6NTomgrBwN9+h1tM7OUSHIDz744KnVU42MLiWib3oZNKanN5XmPOhs0nbt2okKoPSBcHRi4d+Ti1HW+WWsOBaEm7fCHHpSHA0z1ZJWlu2FF14QQ7Xhw4eLSj108Jdl8oGiv60rFoyIoSSSQfXOfvzxR7sX7Ugv+yaZv/kLv4yx033w84nLcNT3NkVuOtCLpKHVAxSRKL29Y8eOp5YXtnXFglHRnUS0R4ZKQumN0xsmokWrDpi95TgSUjlFLisgiWiC9eeffxb3NbLDvFKDJZKjO4lows768Cl98BBx8Q60xw6wRHIcKhF9C1IG6/bt22KcTn+miTz6SY/VRs8bfa5BD7BEchwqEc0jUNq0a9eu4rQ1+lm9evVHj//3v/+JRilUWjNH0lEttcOHDyt/A5OVfP755yJpYwlLpIHhHNVIoxtaGqvv27dP3PDu379fPKZNW9ToebqOoOUkdPbosmXLxLosbulrtDqBkjM0JUBzRrJrrBv9Dk3A0iQ3nW9kCUuksXsi+pYjiSiblho0z0FvJi3lodUL3NLXaI6IJlHpg5+W13D69OkimUOT2i+99FKKlQwskcYkoihDEj2pCgx9ixpxOX1WQXNpNDmqRva0QPdCJByd52o9lGaJNCaRWpmmYcOGYkWwjPTOEzHJoUjSu3dvsU3haZAYtMSK1h4SdE/EiYWUaEYiOmGN9pyok4CXLl1SnkkOS2QbNGSmRaJPg7KhPXr0SFbWirNzcjQj0d69e5OtyKb1cDJYItugXauU8Uwt0hO0xYQEGjt2rNKTBEskRzMS0Q2vKhC11Ar7GVeiWBzevh47j19RHivE3kegvx/On78g6sZRo926/tduPlo6dO6X1fD6ZCCGTVyMy3eevM2CVinQXqDUatDRHB0N4awFIlgiOZqQiOZ/rJfmN2nSRLokxagSXdw2GcVymvDaZ8m3sd88tBSvuBRE3rz5kD9/fnPLh9y5nFCp/VDQKaihvj5oVr8xho+fgk+7tUSrPpNx8ykHd1Nqu2fPnil2tpJA3bp1e3QPZA1LJEcTEtGb5+7unkwi2kxH90nWGFGiB9cO4fXSSUPZlkOSZx73z+oNp9yuGO2zHTt37hALRX/64Uf8evyCWAm+elRHdPLakHRxmC+a12qMn64/efM5DeWoXgLdG9FqEIIkIIFoCiE1WCI5mpCIVljT7khLiejUANnRG4aTKDEMYzpVxfOvNsErrvnQ1GuN8gQRg9nv1UDRSj2TbeSz5MK2aWjUoDXmLl0J74Gd0eSd4biWhg2llOqm+R/acEd1EShjl1oEUmGJ5GhCIprUU+Wh40DUP9NmNWuMJtGeb7qjcKkG2H7sN3QsnwcNBlsM5x4E48P6LqjQcTROnzyAzd+vw9ZdBxFyzzI9bb6X2jATPbq8hfc+m4DfQ59cO84a2ipO2yEmTZqk9KQOSyTH4RLRNyLt3acCI5RMoIlWEoX2/FO1HsoUWWIkif459i3KFCyEYRvMN/nxl/C6mymZRDHXfkXtwibkKuKOl198AR6lSsLJlAMe1Tph2xnbzzylDz5FINrAmBZYIjkOl4gkoYoytE2abnSp/BKVdaK9+x06dBBvkiVGkehhhB+6ehZHnffnQuTTos6imVmihl7rxfNEhP8uvFmnNt4cNBVnr99BVNR9nPddierOOVGkag+cj8j4/ljK0tFC3yfdA1nDEsnRxHBOhQpf0Opty9MCrDN0hpAoIRI+AxrjGY+m2BdwF//dj8SdgAN4raQJdfv74F5kFOJo5575//2BpLTv4Xl9zMPdPJiyO2NnnlKhRRIorRFIhSWSoymJaD0X1TJ70jZlI0gUe2sfquUx3/cVLo2aNauj6quvosorL6JgbhMKPOeOqnU7Y9eVKCQmxCNBkmgL3u2NvOZ7Rq/1J5WetJORCKTCEslhiRxA/H1/fDtlHEaO+FKkmocMHYovPumF0gVNcKvWGkNGzcD524n4Y/UQuLpXwnenkufm9k3vZo5ERbHocKjSkzZIINqblZYkggyWSA5LpBUe+KGZeTjX8ItNSod5eHtmDTzMEce9+Wf4M4Tuie7Bz3cFqpplK9NiCELSURuR1sJRldLJkycrPemHJZLDEmmEhLBTaOxqQr1Bq5QeIhFH14xDheL5ULjUS6hVsyqey50DFRr1xtGgSOWap0Nb7GkIl9EIpMISyWGJNMLDhGgE/X0egTfuKj2PCQ86i43LF2DqtFnYtPsobqcjAtFqEBrCUeVYW2GJ5LBEBoYiEA3hbI1AKiyRHJbIoNCaOBLIHhFIhSWSwxIZEDWJYE+BCJZIDktkMDIjAqmwRHJYIgNBAtFpdrSgNzNgieSwRAaBkgiZKRDBEslhiQwAnZua2QIRLJEclkjnUASimgl0PEpmwxLJYYl0DEUgqk2RVQc7s0RyWCKdQgJlVQRSYYnksEQ6RC17RXWysxKWSA5LpDPo+EwSiOr0ZTUskRyWSEfQEK5z585ZHoFUWCI5LJFOUAVyRARSYYnksEQ6gGpPUBbOURFIhSWSwxJpHFrKQxFo5syZSo/jYInksEQahiLQm2++6fAIpMISyWGJNAoJRBFoxowZSo/jYYnkGFKi+JgIhAQnHaeYEBWOoMCruBP9uPZUZFgoAq+F4EHKQyc0AaWxSaBZs2YpPdqAJZJjSIkCDs1B/Yot4L3AGx0aeMLVxQWVG3TBj8fPYZfPSNSrWh4uLm5o9M5QnL2RvtrVmQ29BjSE08I9kDUskRxNSXTz5k1RG/ratWtKT0rSItGVX6fB2WTCs2WqYfSctdixyQcN3fMgX1Fn1GjWDYs37sD6eZ+jsPma1qM2QysBSb0H0loEUmGJ5GhKIvoQUS1uyzLC1qQpEvl+g2fNgvSadUjpAbaPaQ2TyRnfnopQeuIwtGkxuLUc/ujEOUdCEahTp06ajEAqLJEcTUkUFxcnDjy2PsHNkrRI5L/fG8VMhTHj4OPKob9M6QKn5xrh6D2lA7GY0KksSr4+xOESUQSmCDR79mylR5uwRHI0JVFaSJNE+7zhkqM45h6lAxmT2DO5M3IXb4KjEWqCIQbj3igDt+ZDHSoRJREoAs2dO1fp0S4skRwDS+SCOUf+VXoUiVwa48hd7UhEx2mSQFqPQCoskRyWyEES0RCOBJozZ47So31YIjmalCjhv3D4blmCvt074csFe5XeJNIi0d+7xiCnKSemHLip9ADbRjeHKeerOHBHlSgawxo/i7w1P85yidQkgh6GcJawRHK0GYkeJuLm2dUoa8qBfstOKJ1JpEWiO0FHMGvSLJwMfnxUZcCRzfCetRrBMWpCOx6HNs7HnLX78XgaNvO5ceOGOCNVTxFIhSWSo9nh3I393nAvXRd7rhjnzFY1As2bN0/p0RcskRzNSrR6cHOUb/YR/rE6llSvElES4Y033tBlBFJhieRoU6LYQPSoUwadRj4+8EpFjxKpQzi9RiAVlkiOJiW6e3YDKpcsiRkHHs/zqOhNIsrCkUALFixQevQLSyRHkxIdXvQ+XMq1w7nkt0MCPUkUGhoqhnB6j0AqLJEcDUoUg/EdXkDVXrNgdTsk0ItENIQjgebPn6/06B+WSI72JAo/iHpurvh8lfx4eT1IpApkhCGcJSyRHM1JdGXLGJQoXR27/R8gIT5B6X2M1iUKCQlBhw4dsHDhQqXHOLBEcjQmURwWftQYHp7vYNP+X/Dbn6FK/2O0LBElESgCGVEggiWSozGJ7mFqr9pw8fDElHW+uPsg5VoCrUpESQSKQEa6B7KGJZKjMYkeIizoAk6euYCYVNbiaFEi2kRIAi1atEjpMSYskRztJRaegtYkoiQCCbR48WKlx7iwRHJYIhvILhFIhSWSozmJEhMTsWXLllSLlWhFIjULlx0ikApLJEdzEsXHx4uKP0eOHFF6kqMFidQIlJ0EIlgiOZqU6KOPPsLx48eVnuQ4WiKqideuXTv4+PgoPdkHlkgOS5QO1DT2kiVLlJ7sBUskhyVKIzSEa9++fbYbwlnCEslhidIAJTlIoOwagVRYIjks0VOgCET3QI68D9MKLJEclugJUAQigbJ7BFJhieSwRKnAESglLJEclkgCRyA5LJEclsiKoKAgtG3bFsuWLVN6GBWWSA5LZIE6hGOB5LBEclgihatXr4oIxPdAqcMSyWGJzKhDuO+++07pYWSwRHKyvURqBGKBng5LJCdbSxQYGMgCpQOWSE62lUhNYy9fvlzpYZ4GSyQnW0pEEahNmzYcgdIJSyQn20mkCrRixQqlh0krLJGcbCWRmkRYuXKl0sOkh/RLlIjwG1fx999/i3bxormZf/oHXkdUyrqcukUzEqnH7lONhcyQKCAgQEQgvgfKOOmXKBLePeuhePHicHV1Fa2EuZUs6Y4qtVth7hZ5qWi9oQmJ4uLi0K1bNyxdulQ8HjRoEPz8/MQH38vLK1nRkoxIpArEEcg20i/RPXg1LgZTEU9MXbIcK1csx/LvlmHe9AloV7UETPnKwefgdeVa/aIJiSj69O3bF05OThg5ciQGDhwIb29vlC1bFiVKlEBERIRyZfolonug1q1b8z2QHciIRF80dUGeV3ri8RHUScRf3YbyTibUHqD/kYFmhnNbt26FyWQSzdnZGTlz5hR/pghlSXokojeYBFq1apXSw9hChiRqYpaoUi9YH9cWG/gTXjC/vy1HblV69ItmJLp8+TLc3NweiaQ26+0IaZWIlvLQEG716tVKD2MrGZFoaHM3OLnVxbx1G7Fx0yZs3LgBa5fNQddGL6Fiw944FRqtXKtfNCNRQkIC6tevn0ygHDly4NSpU8oVSaRFIn9/f45AmUBGJBrRthxM5vcxf4FnULDgM3imQH44Ke9vvd6TESI5DVFvaEYighIKlhJVrlwZYWHJBwJPk0gViCOQ/cmIREOalYBTuXbw9QtAUGCAuP7iuVPYOG8Yyj5jQpV3J+BWnHK5TtGURJs3b04mUffu3ZVnHvMkidQsHAuUOWQssVAceSp2R7DSY8mS/rXM73NpbD4r+139oCmJLl26hPz58z+SiDJ01qQmEQ/hMp+MS9QVVyWTq98Pa2Z+n12x9uRdpUefaEqi6OhoNGzYUAiUL18+HDp0SHnmMTKJSCCKQGvWrFF6mMyAJDp5MvkEKR0t06dPH0RGRio9liRJlLtCF/hFxCIu9gEePIhF9P1wnN61GJ7OJhSu8R78Zb+qIzQlEUFzRCQRZeos54dUrCUigVq1asVDuCygR48e6N+/v5hzo6wprf4YPXo0mjZtipiYGOUqSyIwuF4h8X4Wc3VHKXc38/vqDreSxZE/dy4UeakZ1hzlyVa7Q4LQi04VR2VYSkTDPxrCrV27VjxmMpf9+/dj0qRJmDhxIiZMmCB+Utu0aZNyhTWx+G3rMkyfNgXjx43F2LFJbfzEKViy5idcuaX/9DahOYnOnz8vUtv05sggieib8O7du+KQYRaIcTSak4ighYq0gkEGyUXVeGioZz2HxDCOwOES0SQrbY6jNXM0vh4xYgRKlSqFrl27Yty4caJfbXS0Pc0lybJzDOMoHC4RLT49cOCAyKytW7dOtJ07d4o5IxqqqX30571792LHjh04d+6c8tsM43g0OZxjGD3BEjGMjbBEDGMjLBHD2AhLxDA2whIxjI2wRAxjIywRw9gIS8QwNgH8H8wqP/hFLBr8AAAAAElFTkSuQmCC)
physics-General
physics-
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASgAAABtCAYAAAAS5fxyAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AABVDSURBVHhe7Z0JeE1X98avaKrEp6qfGvp9bfVRWrQlovWZWqr9t1rUTFFKUKVqrBqC1KyGmMdqq1pTlVARU4hZDNGaIiGNDFIiMSTE/P7vu50bFwkJ996cc7J+z3OeZO977sq5Ofu+Z++1117bAkEQBJ0iAiUIgm4RgRIEQbeIQAmCoFtEoARB0C0iUIIg6BYRKEEQdIsIlCAIukUEShAE3SICJQiCbhGBEgRBt4hACYKgW0SgBEHQLSJQgks4f/48YmNjcfjwYezZswe7d+9O9wgJCcH+/fvx999/IzExEdevX9csCDkRESjBYcTHx+PAgQNYtWoVZs+ejSFDhuCLL75Au3bt1NG5c2d0794dvXv3Rp8+fTI8evbsiS5dusDb2xtt27bF559/rmzNnTsXGzduxLFjx5Tg5QRS/wnDgmnD0bZFI3z4UT181vUbLFyzB5e1182OCJTw0FCQ1q5di/Hjxyvh6dSpkzr69u2LKVOmwN/fX/WKoqKicOrUKZw9exaXLl3C1atXce3aNfXz7oP1ly9fxoULF5CQkICYmBiEhoYqW/w7X331FTp06ICuXbsqoWPdsmXLEB4ejps3b2pXZg4OBU5DlRefhMVigeVxD/z76YLIxd8tuVHjEx+EJVzVzjQvIlBCprhx4waOHj2KFStWYMyYMapn9OmnnyoxmjlzJrZu3aoEyxVQ5ChIQUFBmDNnDnx9fdG+fXslXLw2iibFzcjEbv8RZTysYpS3JAZMWYIjx6Jw8mQswvZtQP+W1ZRolas/ECdNrlEiUMJ9OXToEEaNGqWGW+wdff311/j++++VH+nixYvaWdkPe15//fWXGlr26NEDbdq0waBBg5RwpqamamcZhGvx6PFWEWuv6TlMXndcq7TjRhLGtvGyipQ7ev4YolWaExEo4R7omA4MDFTDKX7Rp06dioMHD+LcuXPaGfrnxIkT+Pnnn5Xfi72ryZMnK7E1Aqe2TsNT1h5SpY6ztJp7uRK5GuULWFCo2peIv6JVmhARKBeSHBuKOZP8MMHPD35px0RMmT4by9dtxz/J2dtf5xCNjmg6pjmE43CO/iCjs2/fPowbNw6fffaZ8l0tWLDAZcPRh2HlsMbW3tETGL76mFaTHucx8MMXYMldFgGRKVqd+RCBciEnNozF08rJmf7x34p1sWz/Se1s18He0fDhw9GyZUs1W7Z3717tFXORkpKi/FYDBgzAJ598gtGjRysnvL64hPFtKsCSqySWHTyr1aXPgq/fs7YbD0zYrLfP4DhEoFxIdNBY5LcK0VveY7Bj5w5s3rwZW7Zswaa1KzCiWwO4W18rXPlzRKbc0N7hXOhH4uxb69atMW3aNDUsyinws3733Xdo3ry5cqwzRksfJMG3QUlYHq+A9eGXtLr0CVA9rdzwXXG/npaxEYFyIRSofFYRaj52o1ZjTwqGNy1jbXAFMXWbc78snLZnvBGFadGiRcZzIjsQChMFqlmzZsr5T2d79pKM0S3KweL2ClYdvqDVpc8yn7rW9pIHo9ZGaTXmQwTKhVCgPKwC1Xh4gFZzJ9smf6aGej3nH9BqHAsDHBkWwKEcHch6moXLbo4fP45evXqpSYFt27ZptdnBTfzS931rOyiAyZvv16O9jgmty1vPew6/HkzS6syHCJQLsQlUkxGrtZo78R/0kbXBucF3pWO77IxhYu+gcePGKmaJvhghfRhDRf+Uj4+PCi7NDsKXDVbD/Q+H+Gs1t0iIiUBY5D+3Cil/4aMX3eFWsjHCzrvGJZAdiEC5EJtANR21Tqu5zYnQpaj2XB5YClVFcMz9fQ9ZgUtPOnbsiC+//FL1EoQHw0DQiRMnomnTpvjll1+0Wtdx88IBfPxiHrgVqYr1UbfbwuJBDVCg8MsYNn8t/P064TFrW6o3eCmye1DqTESgXEj0xvH4t7VRFX7JC3Xq1MEHH3yAOtbjrf95oZA7Z/LyoL1fIBzxPOSykenTp6Nhw4ZYuHChVitkBUbOU9gZoc4FzK5k9y99lb/ymTdawH/332rt3eXEw+jbxNPaTh5DnscsKP5mS5h4dKcQgXIhFKgi1kbn7lEQRYsWRZEiz1iPInj2uRdRrU4L+C0IgiMGXwwTYMwPF91GR0drtcLDwngw9qbYq3KdEz0Fi0e2UwGbFkt+eNX4PzRt1gT/K1PcWr4VllK0SjvsjTH3cF0EyoXYwgzq+SxRUdlcPMvj/IVkXHXAOlfOxk2YMEH5mriAVnAcZ86cURMMdKIz8NNV7F/7Mzo0rIXSzxfDU08/g1cqVkeP4VOxZP5EeBXzQO5i5TF7k8ziCQ7gfj6oR4UzdPzy9OvXD//8ozlSBYezcuVKNGrUSC3/cWWuqvMJ8YiOicOFy7efZAlHN6Jn25aYsSFCqzEfIlAu5EFhBg8LcyTVr18fixcv1moEZ3Ly5EkV4MrJBz4YBOchAuVCooO+UwLVbMx6rebRYfhAixYt1Gyd4Frmz5+vQhJWr04/bER4dAwnUIzpOXLkiEqExqUajARmV5vryWxpYzn7QmdmZGRkWh1nYTizdfr0aeVEtr2fviAGLNKvYKuz2eSX3vZ+5h9KzybrGC/D99nez2yPjDWyt3k64QxOrB+pnJvVOk5AqPW9EenY/PPPP1Udh2k2m7xem03+zr/La+vfv78a1nF9me1aIyIi1PsZUpAVm6zja+wd8FzaY/pdHvezyUW39jaZaC45OfkOmzyH5zIdCu2xnj0P1vGnzSZfZx2v4UE2+Vl4Px9kk5/jbpu8L7RHu/b3iPfxbpv8zGwL/B/Y22Q7ZNthwGulSpWU748J8+6+Ttq8cuXKA22y/dqu01bHa+P94X26oy1Z27C9Tf40w6Lu9DCcQFFMPv74Y7z++usoX768WuTKRlG7dm1VZj2/tMxnzVks23lVqlRRN58JzliuUKECPD09VVqRXbt2qUbGOr7G/EdsFLVq1UqzyZS1tMmuvb1NflEY/GizWbFiRRXst3PnTnh5eaXZHDtuHM5EbECF117Dy2VfVXW0mZSUpNKa2GxWrVpVNUD6OOxtrlu3Djt27ECNGjVQpkwZ5M2bV01/c7ErQxZ4Hm14e3srm5wet9msXr26SuDGlCP2NtevX4/t27ffcZ2TJk1S57799tuq/Jr1evl36MxnhgObTV4Hz+PMls0m7VAsGYlN+zabzK7J/1PNmjVVmTaYW4o2mc7XZpOv0ya/7PY2N23apPI62dtkCEVcXFzaddIGbVE0eL02m++8846yOXbs2DSbvNfBwcFqHaS9TeaS4v/T3ibTtbAt8P9qs/nuu+8qm1zLxzbA9xcoUEC1Rf4/33jjjTSbbG/MKGpvk/9HtllmjWAdj/fff1/ddy5gZpnvpx3a4/+UbdVm84cfflAPNdp89dVX1WfkA9SMGHKIx8bOG8SDjYdQfFjm04k3mlBQWGY9e0W2JxzLTMrPg08iPrm4eJRle5v8Atxtk7M597PJxkibfBLz97ttJljfH30i6pZNayMnmbFJe4TDCTZMig3PIfbXyS8O4U+bTb5Om+wx2NtM7zp5Ds99WJu0R7sPssnPnJ5Nkhmb/OwZ2eS9up9N3mubTZazapNtjfCe2v4Ge5R84DCFDl/ntfI19oBok/c1PZusS8+m/XWyd2R/nfY22Vvk32ePzoyID8pA0BnORa3s+Qj6g8M5xp+x9ys4BhEog/DHH3+omTr6IgT9wp4ah4Vcy8fej/BoiEAZgICAAOV3o/Nf0D8ckjF3O7N3SsaIR0MESufQ50RxMko+beE2dJpzMkBE6uERgdIxFCcO6xhWIRiTYcOGqZlfszqxnY1hBYor9DntblYYqsCeE+NjBGPDDUaZ613IOoYVqJIlS6r9z8wIY57q1q2rAgIF48MwFi6LYcyYkDUMKVB0QpYoUUIFz5kNBuXVq1dPRQcL5oFBqUy1zOUxQuYxpECxZ5E/f35Uq1bNVAn/GX0uoQTmhVHqzIQga/cyjyEFasmSJWpNG5cX6G9fs4fj8OHDqufEpQ2CeeFsLB9CfBgJD8aQAsWZEVtWQa7TMjoUWSaZY7yTYH64VpEixWUvwv1xqkAlx4djw5rVCNoeinPpBNWmnjuF8KPhiImNQ3TUcYSFHUVU3K11XxnBNUh0INsEigt7jQzXXrVq1Qrz5s3TaoScwO+//65StTDyXMgYpwnUobXf48PK5VGskAcsbnnxZpM+OHjmznzOqUkxmDe8M8qUKo1K7zWD77Ch6NyqPt5v2AHL96S/eSW/0MWL387LzE0BjAynoLnSXsh5jBs3zrQz0Y7CKQJ17lgwvunWDfPX7EF8zBFM7f6BEpNGQ1dqZ9wmYedPKjF8rV4/q9m5c5HW7u9Lj+OJEh9gR/wV7azbMCdOvnz50gSK6Thsq/qNBn1pTA3CXqGQM2GqHaaXEdLHKQJ1+u8jiDh5TitZSTmMWsUtKNVsHO7+Ku5f1A95LAUwLuh2Hu0VQ+pYxecxjPC/N50qcwvlypUrTaAKFiyoEoQZDabSYO8vLCxMqxFyIhwRNG/eHMuXL9dqBHtc4yRPPoL65Yqj+7w9WoWNG5jW3hNuxd/DPrtO0HRv7v31NGZtvXdnV/Y4bOJkO4y47xsXkv70009aScjJ0FlOp7mst7wXlwhUyMJh6PjNTNxK2WZHahg+LuGOcq0naxVAVPAMlMhtQdkGQxB/1xZkjHlilkuKkoeHB9zc3NTvgwcP1s4wBgsWLFDZH2VoJ9hYtWqVcpozGZ1wG6cK1LnYA5g6sA0K5XsCng37IPTknUGVZ3fOQtFcFlRvMxgLf/0Rw/p1RdXXy6Bep28RkXiv/4mxQhSlsmXLqi94+/btVcAmU7gaZTEmh3RcY8fsiIJgz8iRIzFw4ECtJBCnClTs4e2YPnIg6lZ5WfV0Xq7fH/YatXpkM7h5lMCkZYGY1OUd6zl5Mdw/45xHzCRZuXJl1SXmDMiaNWvUotrSpUunpVHVM+wBMl86p5gF4W44ScQ85bJ92G1c44NKjcE39V+xCtCzWLRbE5Ibiej97n9QsGJ7sObmofkoZu1Nfeq34dbr6cCYEduMHb/kNuc4t/fmzdU7fEIabTgquBbu9NKgQQNJsaPhGoGyEh84EnnzPIWZgbe2ab4cEwyvQgwv0BzcN+Lg7fkvFK7RHUmZcM0w/zN38DAK7Olx/zoJzBMeBGf0mNucmzrkdFwmUCnbZ6BkKU/4H7mkykdXDEJeS36MWHNClclK37qw5CkF/8gH94Y4xGOebiPAHTsYUsD97AQhMzBlMHfuyek4RaBSEuMQHh6F2zJzGbN7N0aDblNgS346o115WPJVwg67TtCpkB9QxGJBwxFrtZqMoTPRKGN1Rgtz7zxByCzcMo2ZD7hRZ07GKQK1YUonPG7JgxqNPsf4CX4YOaA7OvUegyOJN5B6KgIr5w7BS/+ywOL+Agb/uAbxF7Su7KXjaFOxACyFX8OIeatwIjHjVCpM6maEhG5Lly5Veatkhw8hq7CNM/TAqCslHIFTBCr59DEsnjMR/fr0hu+YKVixaR+StSiAyxdO48Cendi5ex9C94Zgz59HcT71+q0XcRMJMeHYu2sbtu89iKSLdwVC2UHHuN5n7pilgA5PiRYXHpahQ4dixIgRWinn4TIflKPhTdP78gCus5o7d65WEoSsw0kVbtaaUzOsGlagmIT+t99+00r6IzAwUAWSSrS48KgwpIabgebEtmRYgdq1a5fal16PcHqYOZ4ka6LgCK5fv642XTDKrLUjMaxAcdlLbGz6OaOyGybGZ54nQXAUTDPETRdymsPcsAJF56Eel4wkJSUpn4E4xgVHw9CaadOmaaWcgUMFilPpHNYwaprr5h7l4BQrfzIeJD30KlDc+4w50wXB0XBWmA8/rqLIKThUoLj0hCrPuB9HHRkFqoWGhiIq6tayGb3AiHEuZ+FPQXAGzME/adIkrWR+DDvEo0DpLWWJn58fRo8erZUEwfFERkaq4E0jZO9wBOKDchAcijJ1KwNIBcGZMMRm9uzZWsncGFagfH19dSVQM2bMEN+T4BLCw8NzzIyeYQWKs2R68fUw8T0bDHP5CIIr6N+/vwpnMTuGFSjOFvJJoge4+cGAAQO0kiA4n5CQEHTq1EkrmZdsFajE/b/Du2Mv7DqRcdaCjBg0aJDaVy67uXbtGtq1ayc7cgguhzsccRt1M5N9AnUxGt2qF4bFrRRWHLqVxC4rMH2uv7+/VnI9XBd19uxZ1c3m8I7DTe51x9AHOeRw9hEXF6dyjNEXa+Y1etkkUFexakpvlC1WAO7FvBCgZdnMClzmwqjt7ILr7ZhRoUSJEqhbt67qbrMnxVStcsjh7IML0RknyMybFy/a0kCaj2wRqONBM9G+xzBM8WmFvE+XwcrDWRcoZgvI7hS6W7ZsUQ2FizkFQXA8Lheo62f2oesnrRAQcRZbJ7dGridfeSiB8vHxyfaUvwzMlC2rBcF5uFigUvGDTzt8PX2jKq0Z2fShBWrChAkICAjQStkDo3npJBcEwTm4VKCOrpqMNt3GIEHz6a0Z3cwqUGUQEJ65LzlzkNt2ukhISFAbYcbHx+Pbb7811BZUgiBkDpcJ1MWYHejaui38/0rEzatXcO36VfgPbWwVqJexNDQpU1uXb9q0Se1QzF1SOLTihgQ1a9ZEwYIFZU97QTAhLhOoDZO84ZGvECpWrgxPT09UerMSSj5bCLlyP4EXSr2GDsN+TduSKiM4pCpXrpwSqaJFi+LJJ59UvzPboCAI5sNlAhW+fTkG9emJHj17oqf16NWrFxpWL41ceQrhoxZfYPKiYLt99DKG+XAoSvaH7DknCObExU7yO9ns1wq5CpbDpjitIhNw9s5enHLnzo2goCDtVUEQzES2CpT/4A+tIvMsfj+Q+UAzJo53d3dPE6jSpUurqFpBEMxHtgrUniWjULdZZ4REazsLZwJGkNMpbhOo2rVra68IgmA2slWgHgbmPffy8koTqG7dummvCIJgNgwnUIQ79toEKrujyQVBcB6GFKg5c+YocaKDXLZ3EgTzYkiBCg4OhpubG0qVKiUR5IJgYgwpUFzmwkDNJk2aaDWCIJgRQwoUef7559GlSxetJAiCGTGsQDFZ16xZs7SSIAhmxLACxYyWkupEEMyNYQVKEATzIwIlCIJuEYESBEG3iEAJgqBbRKAEQdAtIlCCIOgWEShBEHSLCJQgCLpFBEoQBN0iAiUIgm4RgRIEQbeIQAmCoFtEoARB0C0iUIIg6BYRKEEQdIsIlCAIOgX4fw1k9N11B8uoAAAAAElFTkSuQmCC)
The radius of gyration of solid hemisphere of mass M and radius R about an axis parallel to the diameter at a distance 3/4R from this plane is given by ( centre of mass of the hemisphere of the hemisphere lies at a height 3R/8 from the base)
![](data:image/png;base64,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)
physics-General
physics-
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
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)
A square plate of mass M and edge L is shown in fig. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° from horizontal is
![](data:image/png;base64,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)
physics-General