Physics-
General
Easy
Question
Four point masses
and
are placed on a plane as shown in figure. If the co-ordinates of the centre of mass of the system be
then the values of
and
are respectively
![](data:image/png;base64,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)
- 3 m: and 4 m
- 4 m and 3 m
and
and 6 m
The correct answer is: 4 m and 3 m
Related Questions to study
physics-
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block ' A ' pulling it away from the other block 'B' as shown in figure at t=0. Extension of the spring is
at time t.
Displacement of the centre of mass at time t is
Two blocks of equal mass m are connected by an unstretched spring and the system is kept at rest on a frictionless horizontal surface. A constant force F is applied on the first block ' A ' pulling it away from the other block 'B' as shown in figure at t=0. Extension of the spring is
at time t.
Displacement of the centre of mass at time t is
physics-General
physics-
Two identical blocks of length L are piled on top of the other on a table as shown in the figure. The maximum distance S the top brick can overhang the table with the system still balanced, is
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)
Two identical blocks of length L are piled on top of the other on a table as shown in the figure. The maximum distance S the top brick can overhang the table with the system still balanced, is
![](data:image/png;base64,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)
physics-General
physics-
A long, thin, inextensible and very flexible uniform wire is lying on the rough horizontal floor. One end of the wire is bent back and then pulled backwards with constant velocity V such that, at any instant of time, the moving part of the wire always remains just above the part of the wire which is still at rest at that instant on the floor as shown in diagram. If the wire has unit length and unit mass then,
![](data:image/png;base64,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)
A long, thin, inextensible and very flexible uniform wire is lying on the rough horizontal floor. One end of the wire is bent back and then pulled backwards with constant velocity V such that, at any instant of time, the moving part of the wire always remains just above the part of the wire which is still at rest at that instant on the floor as shown in diagram. If the wire has unit length and unit mass then,
![](data:image/png;base64,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)
physics-General
physics-
A smooth semicircular tube AB of radius r is fixed in a vertical plane and contains a heavy flexible chain of length
and weight per unit length 'w' as shown. Assuming a slight disturbance to start the chain. in motion, the velocity v with which it will emerge from the open end B of the tube is
![](data:image/png;base64,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)
A smooth semicircular tube AB of radius r is fixed in a vertical plane and contains a heavy flexible chain of length
and weight per unit length 'w' as shown. Assuming a slight disturbance to start the chain. in motion, the velocity v with which it will emerge from the open end B of the tube is
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVMAAAB8CAYAAADUxlMjAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAFxEAABcRAcom8z8AACxzSURBVHhe7Z0HXE3/G8evTYiS/UtkJJV2JIrKaKqEv0Jm+MnKisgmOyt7771XCZnZ0pKyGrQ0tcfnf76nmxJ+SFF63q/XedX9nnNu597u/Zzn+3yfIQBBEATxy5CYEgRBFAMkpgRBEMUAiSlBEEQxQGJKEARRDJCYEgRBFAMkpgRBEMUAiSlBEEQxQGL6HbIzUpGUmIjktCzhCJCamobEpI+Ij4tFdFQUQkND8fjxY7hf8cDxk6ewa8dWuKxejdXc5uKyBhs2boTLklmw7W+Mbp00oKqsBGXVDuhuOQqbTnvhXUQ4wkJD8P59BBISEpCRkSH8SwRBlBVITL9BevQr3DjmiinDLKCtqQmd3iOwbO8FHDx6GEsWL4bd8H6Qk26MygIBBJ+2iqgvrYwhUxdiyxZXbNjgio2bNmOhnRla1K6EmvUlIdNOAUrKylDmNkW5VqhfuxrqSSnA2Lw/hg8bgsmTJ2PJkiXYvmsvrl6/AX8/P0RGRQuviiCI0gqJ6RfkIMB9M2x0W30SycrVRKDYTgpNaggg3bkv1i0YiU7/1IaopBJ6mvXH0BGjMHbsGNjaWKJTy/qQM5+PZx+FT5f1Cs59lKHQcxxO3HmBxEzhOCPlLU7NtYCMWn/suB2Kly8CcOnSZWzdsQczxw6ApIgAoqKi6KStj8kOjti5azcePXqAnJxs4RMQBFFaIDEVkp6eAXc3N8yZMgSyYpyIVhZH74G2cFm7DmfPX8SrwCfw2mmP3kYj4fBvTyjqjsbJJ2+RLjw/j6gn+2CppgC7/S9yB17sgamWEdY+TMh9XJjE2xhvYoL554OEAxwpQdhk1wOybRWgrqGMpqKVPgm7gpYhRtjaYtHC+fDx8RGeQBDEn6bciGnWx3DcPr4Jsyb+i3GTZmH7+UeISUlFoL8vP63uY9kXo23MoC5RCZK6Y3HygQ8SklOFZ+fxBFM6NEaD1q1gty9YOPYlp2YYwWzmmdwHATvRu6s19r9MyX1cmPgbGNvLAI4n/YUDibi6YhA6dBuKg15BCAsPQeCzezixaQ56q0pCUKk2mumNg+OK1RjQvx+GDh2Kk6fOIPFjsvB8giD+BH+/mGYm4t6BhTCSb4gGjf5BS5n2qFtXHIKKImgoqw19kz5YvmwZHnt7I8L3IKw0lDDlaKjw5M/JCTuO/q2qQbSNLMbuCRSOFiYBm0Z0hqnTpdyHqQ8xpbsKjKcfwJuYRKRlZiErKxNpKR/xIeI1Ti7ogxYKZjjil2u55kTewkTT7rDf78c/LkhyjD+22umgqawhNnolISw0FCdOnsGYUcPQXUsFjtOm4Ozl6wgIfoPEwiYzQRAlyt8tpmmxODvfFA2q14aizgBYjlsM22kLMchmMAaZ6UFTXpETrQJT5YRnmGrcCeP3vxIO5BPh547pxm3RuKU2Ro8xQvvOg7H3jg9CIz8gLi4OMZHhCPa9j1OrRkC5nQ7W3ksTngm8c1sK3bb/QFbLBENGj8XYf0fDpr8ZOrRtAhHx1rB19USc8NjswDPo21ENDmdDhCOFiLyJgZryGLH5sXAgG167p0G+cR2I1ZdA9QrMHVAbPW2m4/B1b+RfBUEQJclfLKY5CPNYjA6NGqOl0TRYTV6I0aNtMW2KPa573uD333QeAG2b9YjIPYHTpWRccxkC9a7DcOzBa3z48B5+t89h84Ix6NK8OgTiSph9OggfY55gjkk7iNdrjo5de8DAoBd0tTtCtlld3q9ZR84cjqvWY82aNdy2Fq4blmBodzmI8EInQIUKFVFHoiEUO+hj2prjCE8sEAqVFYzFZm3RTGc8Lr/MW8UqQNxT2Jtowf7AS/5hwuPtMFFRw9DF+3D5qgcO7liPabZ90LwO8/s2gZWDC0IiY/hjCYIoOf5iMU3AwdkGqFytGQz+Nwwrly6C1927wn2MHHg6mUBWbwrybDxGZoIvlg/qBKnm7dGpkzrkWzRA5Uo1odh7AnZcCUBQ2Dt4XL2GFbNGoXWjXPFkm7hEAyhp6mLYuGlY6bIKq5YvhbOzc+62dAXWum7Clk0bsXrlSjg5zcGkKdMwceoM2E8aB5uBVrCwsMCgQYMw2cEeC0fqoEVVASTa6mC8827cfxUrvLpk3HDlhF13GC5GsBX9ZByd0hM9Jh7A5x7ZdAQ8vIzZgzqigqASlLv0wrbt25CYmCjcTxBEcfMXiGk2Et/74fSm+Rg10BLWQ8ZizqbTcFyyGOrNxSGjY4VrzwtPmTMQcnMjuklKoOO/u/FBOPqJzCh4nd4B+zG2sBw2EWNmLMG/k2eh/4D/ob+lBSZMmAiXda64eOkSvJ8+RVBQEN6GhCDqQxxS09KQk50f4P810rhj4uPiEB4WiheBgXjKPcddTujd3Nxw6PBRzJ/nBC1VWYhxgioQVIaIWGPIq2uhu7YKFNp3wfwzb3KfKCcQjkYqGLLhWe7jwnz0whT9lpAxWYDh46fA0sIMhw8fxofYPHEmCKK4KNNimvPxPS6smQCNxtUh3qQlWsgo8lZi3eoCtNXuh+N7FqCfvjFcrkVy8snJbkocXvndxc55gyFdg7MmlaxwzO/LqXRI+DucO3saDtOnw9zCEpPs7XH44H4EBPgjNjYOKSkpyM4uuVjPjMwsxMYn4NqVC3CcZAt9nc5or6iIJlJtoNN/Ai5cu47E+HjuyDRstlFDK3173Iv6WtZUHHbYdkXfeVcQl5aOWzc8MdhmGMbYjcMVdzcEB79CEiVbEUSxUHbF9GM49k7UQjVBLXQyn4ghDqvQ22ok7MbZ4dSWORjSyxBzjt7D5RWDINNKEWY2IzHYQhctRCtAUKkhtAY44rxfvoWWnJyMs2fPYtasWRg+fASGDB2KrVu34kNM6fA3ZqSn4+rVq3CaPQuDB1rDdtQobuq+A4/22KNLM1E07zYUG0954lV8jvAMzsB+exT9tfQw/2zBMK5EOA7pxd90/pGUhrnNeKzacwGBsfnnEQTx85RRMc1C0GkHyNWThInjAUxftQ2DB1lh44Z1SEnNXb++ubgfOg3egHcZEbi6fTasjPXQuasBhk5aiANuD8HsOsbHpCS4urrC2toao0eP5n2cN2/eFO4tnSRx13z06FHOYp6MgdaWsNZqDrUmVVGpan0o61pglP1MODlOhqmKDDoNW4vgj3lWdCZ8jzqiu4oa+o+bBbsRA1CHdyVUhZzuUGz3CAZJKkEUjTIqph9xYaEZmrYyR48h4zB9kh28vZ8K9zHScHFqD8joT0OeNzErJQFx8UnCR5wgxcfylmfv3r0xYcIE3l8ZHV22cuAzMzNx7/4jLFqyBHqaSjDQlEN3peZoLSWFVrJq6D3OBY8i84Ojct64YVQvHYzdfAt8iH92Gvy8vdDHRJe3VCs21caqK1+PsSUI4r8pk2KakBCCiZZKqCbWDluPnEFWRoEI9ewEPDs5DyoS9aA77dgnCzSP9+Fh2LZtG/r06QMHBwd+4Yf5QMsymVlZ8H8eiGlTOWvUqBdWLFuKZz4Bwr35vDjugK49bOEZJRwQkpKchLkzxqFWZQEke05GQMH6AQRB/BBlTEyz8dDrNuwmO8DeShfGXXtiwfHnSMriBCE2DE9unIXzWEOIM39g13G48iZfZNPT07F//37069ePn84zS/TWrVvCvX8Pd728uNc3BsOHD8PePbt5X3AefoftodC6K3Z4fz09aofzAFSvWAf/zllf5m8wBPG7KTNiGvXsIpxG9Ue9mtUgqFIHi7YfwbHVdlCTkYG2UW8Y6KigPmdZCWq2gvmkdfAKzc+rv337Np/DPnjwYFy4cIEfi42NRYMGDfixO3fu8GN/E2fOnMGwYcP41+fh4cGPpYdcxoC2NfGP1iic8i5knnKEXJ6Lzipm6DPBAZPGjsbzl9/IwiII4gvKhJiG3tuLni3qQCCoyVlNK7B/6xJY6nfjvvQrcfTARkwb0Q+mFgMxzXkr3B++QJ6MsiB1tqDE/KKbN2/m0z7zyOKmxitXruR9hU2bNuWtVVbguaTISo2B/1NvvI5KRFLUKzx+8AjB7xOQVYIrPsy63LlzJ8zNzTFnzlzEJUXh9SVnqIlVQB0pJQyasQGez6P4WgEJQe6Y2kcHxiPmYNQgE/59adVGHrM2HAdFpRLE9yn1Yhr/5ip6t+WsUZG2WH3iLvLC4ePvb4epkhLsj/gjKzsdqamfB0xev34d//vf/2BnZ4fAwG8VJQHmzp3LCwfbGjduzFtzjx494gPri5PE4KOwaN8eesZ90bdXB6ioqEB/8GI8+Q3Fnl6/fo1p06bBst8APH18D3E+pzHOWAl164ijQVNpKCirQElBHjKyKlBV04K13Wxs2LAUpurNUKlyVRhMWIVQ8qMSxH9SqsU0JSUGdqbyEFSsh4l7bgtHhWQHYbFxU8ja7EXBCSuzRllJPSMjIxw6dIi3QP8L1ibEysrqk6CyrU6dOhg5ciTvU2Ur5sVBQtAB6Nbgnr+OCmbs9kTw22D4+L9G6m+KRcrJycHu3bthaGSCI0eOcAPpCLp1HEsc7DBi1DjMmjsTfbRUMXjFNXwUXlNm3HM422igCveemE7Z8GmcIIgvKbViykRxysTBqMR9kRWtViFcOJ5H2suz6CdVBar2J/BB+CV/9+4dbG1tMWLECLx8mVsI5EdglqsSZ+UWFFS21ahRg/c5sqlyPJ9xVHQSgg+iW9UKaNl/JYL/YKF8Fr3Qp48l5sydh/SM/BtFygNndGiridVewoE8El9iYV857v0QxYwdwhqtBEF8QakU0w8fYjB+oj3szOSh0lwGE49FCvcIyUnAaUcdVKvQGgsuveaHngcEoH///pg5cyYf1P6zMLcAW5AqKKYiIiKoXr06//PGDVZpqugkBO9DlyrV0Gn8bhR6Nb8d1gBwzJgxGDJkyKebTtKT1VCU+AfWLvf4xwVJfnUa5rKiqCzWGmcuXhaOEgRRkFImpjnw8diDziqyqFpbAua9O0OheRuM3Pa5z9P/2HS0qCKAvM0Gvnzek/teMDExgYuLyy9Ny5kFyoSTCWnbtm2hq6vLh1P5+fn9csWlXDGtDq2Je/64mDJYyNTSpUv59+3GTeZCCcVcvUao3MIYB58VduR+wK5/O0JU2hyde5nj+tXc6ACCIPIpRWKajQdH5qJZTQHqymhi8oJlWDBtGBQb1YaEnDk2XnwIX38/uG+bAnnuGHFNW9yKBnye3oeRkSEOHDggfJ6iw4qXTJkyhRfTFStW8GFUffv2xaVLwqr5v0CemHaa8Oct04KwtFRDQ2OcOXsKCQ9d0aFuFYhrj8Wlgm1WMh5jag8FWCy6iTOeD2Ez2Bre3t7CnQRBMEqNmAZ67UWbegLU5oTzUlB+JSffQ+MgXUsETWXVoaUuhyaNmqGDxVRce5MBXx9vGBoY8IJQXDC/KwulOn36NP/42rVr/GO2qPUrgezxgduhwIl0u+Gb8V44Vlrw9PSEsak59u3cAP/jjpDj/g+iSn2w6shFuJ8/hoXDukPLzBF3QiLgc+0E9LW7QElFDdcfC5sGEgRROsQ0/LU/9JT+gaCmPFbd/txuy4g4AcM2rWExew88zp3EuauPwAoc+Xk/4YX04MGDwiOLF5YxlQfzK7KQqVGjRuHt27fC0Z8jPc4fh1a74MBVv9y8+FKGj88zmPXpj72coL6+sRMD9eRRX6IxpNsqwWDkYly644n19v2h00UHpkbd0Fy8MkSbK2Gjx7fDzgiiPPHHxTQuPh52wyxRgbPaOk78Mpc+0sMRzcSlP+sG6vP0MR/6tGfPHuFIycN8pgsWLICZmRmfUfU34uvrAyPOQj1z7jSyE8Lx9N5t3HkUgLi0MOy17wHlXpNx8dlbxCd+QODtXdBuXhmVmmjguD+F9RPEHxVTZv05zpuPPu1FIdukPRbdKjQBzgnBSrPmqC7VAwef5y4ssar0bNFk165d/OPfCYvVZLGrhoaGfMzm92JYyyIsasHAwBBXrl4XjnCzg6fboSvZEpPOCyv8C3l9YT6acjdB2R6DEFooaYIgyht/VEzZavKocRPx4rQTtKTlscCzYAm8bHjvGIn6FapBb+ZZPvPpRUAAL6Q7duzIPeQPcf/+fVhaWvJhWCzH/2/j3LlznKAa4OHDh/zjD1ddoCEuhpFHC0/p47FvtDq/YGe/cK1wjCDKJ39MTC9fduMzjxI/skz691hvowkFo8m44Pse6Wkf8ODEPKiIC9Cgiz28ubn/i+cBMDU14XPsSwNsoYqlqrImeM+fPxeO/j3s27ePX3h79SYUiPaAtXwNNDV2QWihhIO0gK1QbyCOhi274OqVX496IIiyyh8R01fPn6BbB3l0VFHE2CnzsMM9EHGRvnCdaInOmp2g260jmtUVReue43DtbTISot9jwP/+x8eRliaYm2L16tW8//by5b8vmJ293wOsBiMu+S0uzTdF9UqNYX/8lXAvR3Y0ru2cALk6NTnrVAJSreVxy9tPuJMgyhe/XUzTY/wwxEgRFSuLoKOpNUaMsEYvLU0MmHMIofExeO51Hru2bMbBc7e5x7l+0hkODpg8eXKJNrH7FVi5O2NjY6xfv/6zKICyDvMJz5wxA5OmzEBGhDts1cVRVcoUB30/IjXJHxsmGECqnghqNVKAibkp/qkqQCP5Lrgfll+diyDKC79XTHOSsWKyKQQVasB8/nG8S8tEVmY6oh/thaVKW1ivK5wYDhw8cIDvKf/hwxcNmUsVvr6+vNti0qRJiIwsTWH5v0ZMTAysBw7Clu1bEP9oB3q2Ekc9GS0YG2qhgYgIGrbSgcPu+8jISMNN1+GoJRBAtf90xJbO+x5BlBi/VUy9zrvwX7bW/Rbj5WcdlpOw104LklrTUSBen0/jNDA0hJfXlyJbGmHFUKZPn87XCCjJ2qi/G5btZGRsCq97t5EUeBkLRhpAupYAtVSG4IBXmPAojpwwuFjLcTfLmph78KpwkCg2MlMQFvgEfq8jkVrkm9WfLf2VnRGHl8+e4UVINN9+/c+QjcSoN/B5HICI5OK7it8mpvFxkdCWl0CFBh2w0auQlZn1Es79ZCCu6YBgoZh+/PgRAwcOLDULTj8Da9THwqeOHz8uHCn7sCwziz6WiPvIXC9hWGzSBBL6zl8sSKUG7IJGXQGk1fUQHF26ZxNljexoH8w1aokOthsR+Jkx8j2yEPbgGOYt3IyHoT91YrGTGnEBNu0V0Hv63j+YCZiGW9vtoCLdDeseF99V/DYxne0wHo04q7T9gJV4U+jm+N5zFdRFK6DTjAvI60rMquCzjKOy6oNkPe5ZXv/atWv5GwMrLMJ+FnfR6V8lLvg2dq5agvWHbiHuO9YOKzA9a/Z87rdsuC21gGjFZnByK1wcMR5brRQgqCqBBS4ULlWsfHgC29bcjEB/DrwThGM/RDQOTVKBoJY+jj//s/l3yaEH0KWCALIDXPDnmuKk4qKzCaoKGmPWzeK7it8ipkeOnYCVWTeMV68HzVG7uEl9AZK8McegISqK6+OQX+7Cxe1bt2Bqalrmi2mw2qGqqqqQkpJCu3bt+Or6LIOKWa5RUV/2YPrtZL/D3gnaqFm1Eio10MTK2/9tSUZERMDC3AJnL3gA4e7o06oKN5uYhNsRaQgLDcHNW3fgdukUpvVqA0ENGbRV74ATnEX7Ny3K/U6So17Dy+04tm7chIOXHyDI+wbGtheggdFC+HwqYpaJ6Ld+uHbuMLasX4O1rjtw0t0Lr6KEFmh2CnxOL4Nlhwbc/6Qdhs1YgWO333DjCXjmcQS7Tt1F7GcVyuPw8OIxHDp5ExH8cCoCbp3HiXNeeB/zFg+ucNfj6oo9J6/hRRQT5mxEvbiHk/u3YdOWfXB7EIyE/7AXksMOQ1+kBpRt1qNgU/GshHfwvnURe7dugOu2fbh0xw+ReZZVTiaCPI9gx+HLeBFTeCoUibtn92D3+SdI/JRDk4KwgHs4e2A7NqzfjEPnPPE8rGBuZSrcVvRBHUELzLtdfK3NS1xM2cKRZb/+uO5xHoEHJkFBXg/Ol4P4Pk0ZsUHYPk4HFQV1Mdj1Dj+WkBAPa2vrPx6Y/6uEhYXxvZeaNWvG95gSExND+/bt0bFjR36Mier793+25Enc423QEqsFnYFW0GjTGO0sViD0O0ldrIJW794WiImNgvehKWhRuwakuo2AqdUQmJvoQ0umHkTqSKHHwH9hZW0FE2Nj3qL9G2NxS45shFzfiL4azdGohRL0DAyhq90ZXbR0oNBYAEmzJfBlOpYZi6vrx0C1pSRaq+jAwNgIvXQ7Qrp+LTTqaI1jfh+QnRmD4wv/B+XmotxsoSE09CwwbfsDTm/8MI8zYgRtRuJJVMF/ug+maP4D8ZbWuMoH00TBdYgG6jVWhomZHrro6MGwVzfINhKFdGcrODk7YYC+DnQNjKCr0Ra1azaF5fyTiPqGoH5NTGOeHsXYXu0hKSUHnR6GMOjeBbItmkPVbAouB7GkmCw822aFGoIGGLnpwWe+1nceK6BUoxK0HM8jgRP/rITX2OPQF22571h7Le5ajXpCS7ElpBX04XTgEXJvMWllU0xZKTu2wp2Rxd1RcqJxdvkY6Gl1hbnVYJjryKB6taYwczqKUGFBJjYtZtXyi6tdyJ+AhXAxN4WkpCTfn59tysrKkJWV5QWWWd0tW7bE4sWLhWf8AbLjcHg8Nx0X7YIdj9/AbXY3VK3ZBk6X/lvgMzIy+Myv2U7zuEdJGKyvgEZVBWjcQg69TQy5D68lHLd7Cj+0nAEbHo6FCxfy7wE7l/g+2e8uY0C72qgpY4F9Xm/47L+M6ADsmWmCegJOTC2cEcAZ+znvzmCAfDOoWy3Cw3d51v9HPNg9GS0qCdBh+hnkegPicHC8MgQSveGWt16Y9BRzejExtcXTz8TUF1M5Ma3XcqBQTKOxaYgKBIKKUB+5Fb7R7H+Ygac7RqIBdy0VmupiuXsA2F/PiHiAmV3qQCBphOO+X1fTgmLKf9KibsBWtT7qyvfDwft5wpaDN3e2w6xNdTTu7oRgzqjMjveCbZtKENedgSd5RmZ6JLaPlIGgXk8ces7mux9xaX4P1KzREqPWX8N74cctM9Iba4aoQqSuPJyvs9lXNtzLmpgya4SlXT558kQ4wkhF4M0TWDXPAQ6znXHU8/mnKkovXrzgF27Yz7IMy+FnRVFatWrFiycL7WIbi0XNE9M2bdpgxowZwjN+P0m+u6BVuyLkhmzAezZzerkHncUqolXvhXiR3yX7q4SEhPD/1wsX3LibxnJoyktj1JDBWLF+Nzx9Phdj1hLGwcGBr+r/N9YyKAle7h4OsRqisHQpFBEScw8jW7Np/iL4Mu1IiYC/tz9CYpKQHv8O/k/u4sqF09gydyRkqgkga7tf2B8tDDtGt+dExwinngv9A0nemGvYGIK2o74Q02lazVC/9SBcE4qp6yBliIjIY71vvjsgK3gb1GqKQMVmU4HutWm4OkMdArHO2H3762nWeWKqwn3uWABh1JGxqFexEqS7DsfKNSuxZNEiLFq8FKtXzcfAzhKciMvB/T47MgdeGywhUkkas8/l1ohI9NmJLjUrQsP+MBK5S8uOuYuRsgIImnTCuHlrsHLpYizins95xRrMHaYPUbZmY3eWOzMbHqssy46YMstyzpw5mDdvHu8fZIWW2QubOm0GHBxnYa6TI5YtX4mbN28gLib3X86mg8uWLeN/L+v4+PhAS0sLMjIy0NTUhJ6eHvT19fnfmZCyfcHB+ZWwfi/JODFBDZXEVbHqRt5tPg1n7NVRubosZp35/nVt376d9wVr6+hATl4BXTp3hqmZGcxNjdBDX49/vWxjvbVYOxhmmffo0YN/D35k6969+1fHv7X9zPHs2NL0/F27dsWAAQPw8OEj/r31cjaFaG0JjD3C+kgUIOklFnevAQmDBbnT/OwE3Du8BAN6akJZRQUq3Hus2dUApr26QpITU4XRBxDF69/XxJSzTA0aQSA7Gt7RBcXUD9M7S30mphsGqqCOmA72h+XPFlMCN0FNVAydRu9Bfg+KRLhP1+D+jjb23P2emLryQu+3qg9qV6uMVloWGDrIin8f2GZlPQhDR47AsKEz8Tww933IfusOa5mKaPa/zYhOz8QVx46oyP2trQ9y7e+PL0/CSEKAGtIaMB80BAOtcp9rwAAr2AwdjqEjRmH2tjvckem4srIMiSkrALJt2za+uhILcWI57Bs3buSzhS5evIizZ89hy+bN/Djbz9IyWdD7n/YjFievXr3C+PHjoa2tzX9h2KbDic/EiRPx5s3nFZh+J5lB+9G9YSVUklCF3dK1cFm5AqvXrILjqG6ozt29pXovhn9yvhXyNVjPrPr160NdXZ3vk5XXN+trW7Vq1VC1atWv7vvaVqlSpa+Of2urWLHiV8e/tf3s8T97PUXdNmzYwL+3YcfHo0G1Gug1N79yF0/0XQxvUwENjJfws4dX+7mpdtVa0BgwF6duPMbrd7FIz85BxI2N6FBbAJmR+WK6fZQCP82/9FYoiCmcmBpyYio1BI8LduTJuonBsmKo29IGnoXEdF9ovpsm5flGqIrWhabtrgJlMxPhNo2zTH9ITHMt0+hjY1GnYjXoTDnBr5nkk4l3frdx6dojxCbm/d0kXFpgBHGxTnA5tRMWrcShOnTTp2ab6ZGcZdpGgOpKtrj6/vPPb2rkC9y+6o5HL9nVppe9aX5qaio/vWV+0/9i3bp1/IeppAo9/2lYhX7m8mDbnw+NSsLZ6T0gWrE2lPSNYNSrh9CS6gljU0NoKTaFoEorzDz1gpsMfZubN2/yPmHWEpv9/9isg3UjKLytWbOGd90w65Q18fvaMXkbm5Uw10eTJk3QmbN058+f/9Xj8jZnZ2f+HGb9MpeKo6PjV4/L25gfmxX5rlevHu+mYL7crx2Xt7HnnjVrFr+AyGYU33qNeRurZcCs70aNGmHs2LHfPZ5dz/Dhw/kQOldX13xDIv4RputKorKEOmbv94D/23C88rmN9RP0UJP7nkj2WYagFODhos7c96Y2LBdewLvEVKQkRsP/7mnM7KvIf5/kRu1FJG90RmD3OBUIKitgwbG7eBPNnZwThV3/sopfkvh3iztehITjNSdeux0s0bCCAHXkRnwS0/XWyqhdRxt7PxNTV6jUEkXHkTs/F9Opatw0vwt2f1NMD0GvejUo2azPFcHYu5jUqQEqiClh+m72WiMQGR6MO0ed0U1SgFod7eEbmS+zqUFHYMmJ/T8yUhBpooXlNwpUmstKxLXlZhATVEfXUS644f0SkVERCHzgjpm9ZVGxWkvMPMv+KvOZWqC2oDnmlhUxZSExrEkdqz7EpvusVibzhzKrjP1k7TKYK4D5ENki1a+2Uya+T3rQYRi2qIq6GpPwKDYVmRnpvMCnpaUjOzsVIR6r0aGuAGLd5sD/Pxrls/9dw4YNeX/of/HgwQM+PIyJ5I8sKo4bN44Xrs/97N+Gfb7k5OT4Klffg4kVEzuWoRYdXbDc47dhn0sNDQ3+dXwPVjScCTv7rP8I7BrYjebkyZPCkXwSgtzgaN0FLSWl0E5JDarqGtDu3A1qkhVQ32A+/Dg9TA25gmkWHSD5jxQUNbWhq98DPU36Y7zdCPSUrwURtUl4zQcPp8PnxFxoNKyC6vWbQX/sTt4q/BBwDvYmypCQaApZJXV06qyD3sMnoY9yUzSUtYIHr51RWNNPDtVqdMTukAJiGrAO8lWrQ2XoduRXYkjEpUntIajZATu/EWbH4ky1K1ZAuwJxpnGBlzB7sC5aS7WAnJIqVJXk0VKqOdTM7HDsYSi/uJVPIk45dONvFi36rEZ4oTt+TlIoTq0YDS1ZaUi3bQ81NVXItZKCtGIPTNt6DVH8S0jDJWcTVBM0xuyyFGfKVrbZh2z58uUYPXo0bGxs+NAn9pNZKqtWreL30+LEbyArGkfstbkPYhUM3u0vHCxEdghcbVif/OoYuuMpMr+hp2yaz8R06tSpwpEvOX/+PKSlpfljvreSn5CQwH8umBj9qJAyy46Fmf1IxwWWmsxcEmymxOoNfA+WYMEWzRQUFH5ISE+dOoXmzZtj9uzZP/RZZgtz7KbB6vN+s+5EWgwCn3rhqrsbrt56xE3jYxD2/AEe+IciWSgiWYnv4PPgFtwvX4LbFU88CghHRnYWPrx+ilv3nyMlXfgPzEhCiP8DeF7zwK1HwZ+iLdLiwvDs3g1ccXPD9TtP8e5jJuLe+uPx0xeI5/9GJt4HeeP+fV9E5z0XR3ZKBHfeffi8jOKjDXLJQvzbZ7jzwBdRSV+/cWanx8Dvnhe8g95/LpLpsQh6dh+eV9xw2f0q7jzyR0TS1+dG6R9e48HdO/AP+1ZL92xEv/GH142rcLvshmu37iMwtGDxnWzEhwfi/p3HCE38XKp/hRIX04KwDw2zDli4DPv5NxZWLtW888KcfspQ6Dkd96K/bSW+v74RvTXk0GXkZoR84zDWaJBN3b8mpizbi01b2X5muX7PImXRAUzk2CLVj9Q0YDMYNqNhboa9e/cKR78Oi6xgyRNMpFl41o9YpCxGmFmvLC6YFQL/L5hVz8ScXYuTkxP/975HnrXOZmwsEYL4O/itYkr8Yb7/PS9EzjdPYemyTCy/Ft7FFt6YcLE42u8JKZu5HDt2DIMHD/4hi5SJ1bNnz/jjWQuZ78FcTcz3yRYCf0RI2fWwzrRsUfRHLFJmFLAi4Wzm9SMlItn7wSxqds7fVF2MIDElioiHhwckJCR4UfgVfkSACsLE9GfO+RE/bUF+5rnZtfyse4rcWX8vJSOmaW/hcWQ3NnNTvfXr1vGrvevWrceGjVuw/7QngqO+ExVOlHqYmNatW5dfRc9bOGSlEtn0u6zXVCCIolAiYpoTcw79ZeqhRu1GkFfX4FdDNdTVoKwojzbSzSHZtiucDj9F2s8ZJUQpgompqKgov7E22KxtC0tQYKFEbDGJIMobJSOm0SfQS7wq6quMwc3kFD7OMnf7iNc3d6GvfE0IGhrhaFDBaGGiLHHlyhXUqVOHD9xn2VB56bFUIYoor5SQmJ6EUX0RNNWahi/bq6Xh6GRNCAQtsfwROeDLKu7u7ryQsuwgFtTOpvc/658kiL+JEhLTUzBpXBP1ZC2x5fot3PT0hKfnDVy7cg47V0+AVqum6DR0I14m05evrMKm9eLi4nxqJqsiRQsrRHmnhMT0DPq0qI3K1cUgJSMLWRkZ3p/WupUUJEQqoFJ9Ncw54fef6YpE6YbVNa1VqxY/1acQH4IoScu0UU00aD8Ih30C8dzXh6+i5P3kPq6e3AQ7YyU0qNcOE/d9O8OGKN2wYjU1a3Kzj3r1KPmCIDhKzmfaQARNO03G14Jkcp5sg1YDAap1nIkgWq8ok7CSiiIiIryYlvY23ATxOyhhMZ2CZ8KxgsR7roSyqAB19BbhDblNyyQs775GjRp84H5cXMG853zIj0qUJ0pGTKOOo6d4RVRprI1Z23dj1/btfPjMjm2bsHzWOOi2rY8qdVUw52ww+U3LKOfOnfskpoWrfbHMoIcPH/7Rmq0E8bspGTGN9YBdN0W0at0W8u3b8wUj+E1RCarqHdFrwATsuvaiUGktoixx9uxZvig0E9PCQfqsjxdrz0ILU0R5okTElJNT5GRnc9O8TKSnpSKVr5eZu6VnZP18vQ2i1ME6JjAxZbGmLAMqD1YgmbUzYR0WCKI8UUJiSvztsMpKrBUJE9O8WqWssnyLFi1w5MgR/jFBlCdITIkiwYohV6lShW8xwixTVhS5devWvC+VIMojJKZEkWCtNtgClJiYGN9XiRV2ZsVPCKK8QmJKFIkTJ07wGVCsFw9rB3Lv3j3hHoIon5CYEkXi+PHj/DS/du3afHYbQZR3SEyJInH06FG+YhTzmf5I3yOC+NshMSWKBFuxZxWjmJiykDeCKO+QmBJF4vDhw7yYslqmJKYEQWJKFBHWGbRChQp8i+NviWlqKvX6IsoPJKZEkWBiylbyWbZTYTFlLWpYVanw8HDhCEH8/ZCYEkXiwIEDvJg2b978CzG1t7eHiYkJWaZEuYLElCgS+/fv58VUWlr6k5iynvOsqR4bo0woorxBYkoUiX379n0SUxYalSekLDefhJQoj5CYEkVi7969vJi2a9eOL3Ti5OTECykrGk0Q5RESU6JIsBJ7bDW/ZcuWmDRpEl/khC06EUR5hcSUKBJMTCtXrsxvbdq04RvsEUR5hsSUKBI7d+7kLVNWz5S1fSaI8g6JKVEkmJgyn6mcnBzl5hMEB4kpUSRYg0QmpvLy8p8q7RNEeYbElCgS27Zt48VUQUGBxJQgOEhMiSKxdetWXkwVFRW/KaYkskR5gsSUKBJbtmzhxVRJSekL0YyKiuKLRxfsWkoQfzskpkSR2Lx5My+mrPdTQTGNjY1Fv3790L9/f1qYIsoVJKZEkdi0aRMvpqqqqp/ENCIiAn379kWHDh2olQlR7iAxJYrExo0beTHV0NDgH4eFhcHQ0BA6Ojp49eoVP0YQ5QkSU6JIuLq68mLapUsX+Pr6Ql9fH8bGxggNDRUeQRDlCxJTokhs2LCBF1NWNUpNTQ3W1taIjIwU7iWI8geJKVEk1q9fz4upmJgY/v33X8THxwv3EET5hMSUKBLr1q3jxZRZpcnJycJRgii/kJgSRWLt2rW8mGprawtHCKJ8Q2JKFIk1a9Z8WoDKzMwUjhJE+YXElCgSLi4uvJiyUCgSU4IgMSWKyKpVq3gx7dat2zfFlHLzifIEiSlRJFauXMmLqa6u7hdiyuJO2QIVa7JHEOUFElOiSKxYsYIXUz09vc/ENDw8HFpaWhg2bJhwhCDKBySmRJFYvnw5L6bdu3dHVlYWP8ayn5gPtUePHnj9+jU/RhDlBRJTokgsW7aMF9OePXvyj0NCQnj/KUsrZXn6BFHeIDElisTSpUt5Me3duzdevnzJW6hsIyElyiskpkSRcHZ25sW0Y8eOfKypgYEBFTkhyjUkpkSRWLJkCS+mDRs2hJmZGQkpUe4hMSWKxKJFi3gx1dTU5FfwCaK8Q2JKFImFCxfyYmpubi4cIYjyDYkpUSQWLFjwaQGKgvMJgsSUKCJOTk68mLLq+iSmBEFiShSRvEInQ4cO/WYXUupOSpQnSEyJIsHiSbdu3crn4X8LElOiPEFiShAEUQyQmBIEQRQDJKYEQRDFAIkpQRBEMUBiShAEUQyQmBIEQRQDJKYEQRDFAIkpQRBEMUBiShAEUQyQmBIEQfwywP8Bai0Z5TkQFkYAAAAASUVORK5CYII=)
physics-General
physics-
Two persons of mass
and
are standing at the two ends A and B respectively of a trolley of mass M as shown When both the persons jump simultaneously with same speed then:
![](data:image/png;base64,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)
Two persons of mass
and
are standing at the two ends A and B respectively of a trolley of mass M as shown When both the persons jump simultaneously with same speed then:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAX4AAACGCAMAAADtshEOAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAKsUExURf////39/fv7+/r6+vz8/P7+/vn5+d3d3aampqKiop2dnaCgoMvLy+3t7Xl5eUVFRUhISENDQ0RERGpqas3Nzfj4+PT09MLCwjk5OTg4OD09PTo6Ojc3N0pKSqenp+zs7Pf39/X19ZeXlzQ0NDU1NTY2NltbW4iIiC4uLpWVlfHx8e7u7sbGxs/Pz+rq6uLi4u/v787OzlRUVDMzMzs7O6Ojo7q6uqGhocnJybOzs3Nzc9zc3LS0tIyMjH19faurq9nZ2ZKSkmRkZHV1ddLS0ouLizExMU5OTszMzE1NTWZmZlhYWEFBQV5eXlBQUJCQkKysrCoqKsjIyExMTKioqNXV1WJiYtra2unp6eHh4Tw8PMXFxSwsLMPDw1VVVdHR0YmJiVpaWtTU1Obm5tPT0/Ly8mFhYfDw8Hx8fLy8vG1tbVFRUS0tLYCAgL29vb+/v0dHR09PT4eHh97e3o2NjXd3d5SUlMfHx3FxcaqqqtfX1y8vLzAwMEZGRre3t2BgYH9/f1NTU2VlZfPz82hoaF1dXYODg46OjnZ2dpmZmcrKyqSkpNbW1np6eqWlpYqKiuXl5WdnZ0lJSUtLS5ycnEBAQMHBwXJycru7uzIyMj8/P2NjY8DAwJ+fn2lpaa+vr5aWlr6+vufn51JSUt/f39DQ0Lm5uXBwcLW1tbCwsK6uroSEhEJCQrGxsX5+fsTExOPj43h4eFxcXLa2tuvr64WFhW9vb6mpqdvb29jY2FlZWWtra5iYmJubm+Tk5Ht7e4+Pj7KyslZWVm5uboaGhigoKHR0dD4+Pl9fX5OTkysrK+jo6K2trfb29mxsbJGRkScnJ1dXV+Dg4J6enpqamoKCgri4uIGBgSIiIiQkJCYmJikpKSMjIx8fHxwcHB0dHSUlJSAgICEhIQAAAI1g7skAAADkdFJOU///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////AIqL/3IAAAAJcEhZcwAAFxEAABcRAcom8z8AABKBSURBVHhe7V3NmfMqD82OPU2wYOkm/LgIumBBCe7ApWV1a/nOkQTYM8m8yX2TjH0/n8k4WPwYhBBCxs7lxIkTJ06cOHHixIkTJ06cOHHixIkTJ07cR7TvEyf+v+DKPM+LnZz4MOLkgWm000PjgDp0HAaPT7HTIyPG+/zfZ8/ESxiI5IzwX0XcaQco++f/gO0jTbjTjjj+nnaVMenuVGxMZP/RdU8c3TKPl2UutzsgTr80vksoeSouTPlO/1P8/dFn3tFPaZjmdLcl8y9JWLhO44yp1SXP/v82O7l5GLJoxjvD4xBYrjmOPrkYKOXuu6r5aVp+J9jtbpgiAgs4PG4HQVwgNWS/MH85lPkfoU8rT0c2bkpoLsR/hC0ddjKeAyvmMwOoUZy2gxCa/wrdo2wfE5IdB7FJEqQKQztOE9m/oI05DWEftg7Zf/GoWAH7HRT9bBGCETY/EKQJ2Zc91Phh5M5iNyKY2Eq/jGC9m3YynUEcVPoZCFhibaR/IfOv12lZwjxRRR0IY9qu1UX6ix/LBPXP1u4BhcpH5AKBEOaN9Lsswj94nzz+d6IvHwQMiq59nCkfsJ9zwiXsRfqpfAZKP/vhUq5N+lHJorqHSHkvs9WDwLRVXSXg/mRTL5QPKc7vZCQvVD6cU5fEii0b6V+E/TikvDiYZvuYrh6Dm4T9WmFHPTSjaS6xS2LoUb8Lt6AWI200zk5f2O9gdcLyOaTLB4rTpH/N5iiLm3DdqQ03+g37KfwADf+jgaIDi+0Wiufsu0e4Lv1k+ZInupuPpfW16rFMtxVMFAP6l1a5f0DcKp85jEvIGWaDUQ4C4f98e5lSBp+BcY9tcmvlw9krlHHErHA8YJWY8q2aiw9xoMG3Q5RWLVihqOjVTxjER+M/bIiJlb9lM7iyELsf0YsXu/OaDij8kdwH7ky+RwAdPjQ7D+VoM4D9nirmyOwXdyfUv50fCXEWBX9k9mN1Ivyf7PxQ4NCF/O9zgn0IUW6zXw/m6DSIr/bQG2T0Ljtsn534R56Bis4x5y0Dl+2AP6L4R3WVH3LeMkB9UvWjEdCgB+sBY784C4+oO9v4xfR7QJ/PkmTqPfDcqwIkpidvxBwLM61OVh2Sc0DpR5VHqT4Pe3XP3gcXvVJ1KJ9j6h41fCbRQO8x3+zeGb/kTtqrgJJivvo5h3Rg5UOHG3fFQP3M0qbXI5YgPTvS//tKFJprMUIFhffU/O3g+L1m7n4bru/a4Iy+FZ8kevqFA0zdndSYY+Ki5YD8jwsm3iu3llD7rG/BvA4RK4srd5ZSVbxSv8Fmo9iL6Xy8G6Wor5sTdI6YDeiG95kPkFIuqTHLvHR6Adt9QI05gg/oLneZZoPsPHFoyds2OpDvkNLF+9c6Z8ZkT6ON01429DwDKhyvCp8TMFrwpjZMaYKCyym/Vvpjabd53bEezGFlZXOb6Pt4yVBCb1OfMaXiS5zy/D7X5L3HdvYLEX5bryDswf43tWGanM+jn7e7u16BwzG9YfRXc5SD7TD7NzuvXgiUnpLLafZjedPKTi5ioUPAlUJbp3KDfjc5eU8jpuSK9ykur+7iowr/LL6Sxgzx+b/N4xanFEcs7i7L26T/YOAiV1aMynHes3uf3yRO3kG9zZfxyPfEXwlIv1/taBYjKLxnRyTUcqZXA53t5tf6fA6LGWZIoq1joN2f5j9z50b/PNBl8jzn33ftvyuh5npJFf4eYiQUrLGWHCj+UqdYJq57v7CfScE6gZE0uWJDF0gG8St/jQE0qkfgWz/1GkoGJF2lCmrEGk6OFqNxjn/AqgCLJdbh38MYIOZLKQv+cJwDjqXMU0ophFkiDAHnIU9ERmr5zDPSKkJGXBi5lZKpZ/6BOCMXIuZxtEtoxJyzljVrckawENQGBTGG1yZp5lVzYFrUKaUpoIoSASrKQFoso5P305yR2xBAYnq+GSe3q+3v/nXBrIsqYrLVW0UVcooDopQud+CRFke2SRN0SDQjvtAV6whJCeBcqF/IXyK0XCUqXZMrGNFgNE0LCPMT/pSE4/7uwxRo+SySQlmSD0WQYo0xANmCuEEcSRU65XQpkCTIHSgSI0IrERCziR+RYpZi6UslC5TKTcejK41YyYwYnYMskyqDRfcngwiMkloKr2nxh7il0hYMQU1L5RPdIsSy5B2yf4EFLhrylp/EwT4hfaM0CVBVk36JuaFjFRphJ4bvqTa4G/2HfHchT5PvDOPvbqh63bX/XFJYrfMkNURCTn4RhTcX7+DJymnyW226VRBpRscXc3F0CKV+CyyygwOpUpVusdtkHZW6lf57qT8LebPJC2pyq4Q1bQdtXb+/R6qzgzpB+fDhe/7phzoaNvNIMCTnSCFfnOQsoqavkBgpyRITNb08PywUFKFfivrkttA4T1a6XFuB6VZJMgEvmlAjEAMyI0qRHJISwORLIv/mxQrdTr1IbKFfANsscDDKqvHBh//ERKGJTdNNImAyq90CuhpzHksCpYNKGwjmkeaAUS6FWCnV8h4kQqKYlBEk00BMtRShanKxEr8WYrbjMAiFdL0kDVKBV5KWYEQ1W1uxTfrR+BgyzSaGjPg5uIl3pTVUDWP7r5DWKdEPV4E0hC1HBKNwsMS0rmX1o/QVGUSyRTJIcZXOgvhRqtFJ1Utk4euKysTskCw0pTJhQuX4wTVI1MshKXuPUoI1V6Vt3nbCHRe4wOfvS+KCWGyhKnJlDGEYxhyoBEYygNEqHggMaRLDcEXD6AcSVYEPR3VLDn3CDweUPUEIWClc+PMqWPM2OqMI0i/UEVQVSpUMPQJkKitetQH6RcgawwdhsWLJvM8uRdxQKRtKPeHrfdg1v+H1Rp2fuCxShyW64t+09+evkAeR6dE/adRHfU8X37OkhI8hXmYf/LyVivuI4L4kDTvcvrTUPT35WdnQW83vu+N5H7zdyhfdPIbWQnvx4Z4A0TB9Pj4rG+UaoOemX2jS6MMlPHw/a75WuQq70z6xScSTL0WNkCrO3rzj9ukhzXeIPXyrL9bFImp83dftQUz1uqGNs34YnpPjMtBM+gWXS8wwqmEwPFjdvlYfMV4tuBO4vhkyc1fqE1iGAMtp/vzUyz3AtLQfq26TfqqhX7DSfkRn/9MTk066Ln1c/DHnw3Iuj/Y7VI4mjNP+Hvhq01F59nEotXxghXy4RdA9UtHJP3Jhvg3WxB8t3BnzKRt6S9px68pTWGAqifKx80/B2Z4Ge78iOfwzSkoFK018VS20I8xpwuq45PSY3dkTjepUevETTn+Gs43YUR0LEv4CLN27WwA15XMX12tSZyOwygSSEekyaBEk19SMMDJB70Qlr14rTm9GJ9ccKxqp47j0dKQ6N3txR02lkiyhOD1H3tpnKiNuWgsGrOv1Oyg56N4D3rJVvyS3FSR8Mqm8C8u3zFzNpUiXGG/MSmJKkILpJUK9pKSbu5L0xOSIEe+p+Tc1gsm5D0FQi0nJT53GtEokxJkmNKFWf6d4Qo0mZPrT1J23Iu5h3VJFQL5jgugIxHF4vf7zj0iTHOix1TP9UyDUYtYQugaAfwAZNEwsyRlmrERrWjnoqR2lEHGONlol0lMqpRhZQf6L+1MyVBr5LiwH01mA4YuiBwc24+Ez2PA/0I+s4oQai5N2Dv46UcBRebQF0koRna7cMcO9BIEJAYghhI4JMUr8NXNDAxL7K7cIcd8BsnBolaVAfVFsKeceWbh7oZQJKoMyHvgwrpRNF+QQ5C4Jy7brzWmgb557GvKAESZULFxYMqiz9wUKCSM4eGYW0BUnd2WgnTwvBlr58sjUL7D+G1waZlHU0aW2rMpXMXKg1tHeUZ24K6cisxB8DNvGM5YHGUciNAtp9HVxgcxgEUDnWJVBLDxJAW1pi8BYf00Al772BUfNsrSynW+Gfv8Bgu542ySsMwwt510wfYVe0aUtxaCS7K04sOhq0+dmWvf786VlQecZE3oIfKtZ5uYSQ0/UqzRuxdzsRvSJZVlxMDUP1dRkIKz6pBrv6O8bfdLK7iXuBahOqNwCExpbr7XBqz5ptnUTUXFgaAhZKt9mjBgNxSQJUSgGWWVHaFfpfLsh/qsQfd0WormuobFnSbVPVllKr9i6G61iuwE0SNt9J4pIaOBRbVzo4tjuli59sU+aKBDrPH4wYlgM0GXZQqBrT0iCfvcbmfkFqvVJDwEb8a8c7A7Y9QDesFrCJgOEZLEEu0HW13bif2k9AfUjYxucFa+sYG7v98wSyxPQjMEjn80TlKHpFx0xSIhiatOhkqwY2+SFf6gky4yZpXJrPWJqh9Z5IHLFK1no+OwjtPVOc5THrqa4r8OC+4HDZGmVnj1mWgmNydurERjS2RezqmxDF5rdpOacW7meamj206qYVYECaCwrBnqqsbVxBglNBtSRwwROtIqEejGojWXW95PzZGlvKnepqkBkrmMH4m9Z9oQuwir/1k6rNHWShiCFEFeNXdGgdKRRMvQlpOpfEorG4jv0ux2kM60knNbTtFBYTNdYbZy0zDoZkSyaXuMxBVlC9IkVrYqIQdViDO1Q+wPgRxUkqPrWzs6PxrjGdaFJvPO3p2TNTDuUG68QVAYz1C0UFNOktU8ELfO6d2xocexoLOcT624psIcUTeir+CNBqHXdD1Ar2uXKGVP1CLKdEr9iZp1BgW4m9R+s6Ybm4uvYQZ+YqOucK1AWbi5C9cNU+O99YjQQN+JvsahrvUjbMYJQZXA3frpjEzJVe2cvYAO7sag9QaCdVXxSm0HbJFiXXJC/1hP0+2oIo6iPna5LGCJZVRJhbAWxjyz2Dr9Q9NpqsQuzx6zo2jsspoVktDHUNQ3mZrSERAiDhXYFstCCZnOiiqLpBViv15YIQ0heibr0E2mlram+iTogdpAEoyzDJNjtEqwcjCbKWkL3tT+hbBW0H0VbacBumq6GRGvnrgB5tBp2s13mVw2yJzQEEdaGyoQBGj7dbOlCr2YLwR+u5LdokDaeKpNw4Wqg93sm7b7mSvt3NTW10HoJ10KNNrbHNbtR4Kba7/sC2Cqskftb1mTIo7ELqqYypC3iu35XPwMbBWYabc3MLo9KQ8qmjmP36HRl3RnXN0KN8gNQRFFJQYpxqtdwqWokF6wGl1hsROAitVaXzc2HvQBV79LV2EDTWkPgtYZQ/6nS7J0wyLsk/hgVQ8YuhEb+jo2EXK6L6TErGyCAxhosmjY0S8hfSmXwEpfGLrmbQ9HlD14ZbEjiuKLJR/7rkd8S6od9gWyosnJpTXbtd+u2bLCmkefaoBYZq+hVzhA92Gkdt2gP4W5hXyJqfQ3/+nrvxc3W7LSu/0l8jNfSqx/u2QMIkgzTt9VzpQRMj38K72zVS8FfGX4batHoh49yw4nhc4AOcM/tFH4Ka4PFvj+E2By0+0St2+LbQvdp/Cmf3uqt6VpqBuo/Id8t1rBOYOinXxNvIVnT4CcxjfcLaITZf/vVN6m9Bhuow2+35X4L7+ibexnuF/RvAPYP9pJbo+wMrNY4ca8M2E85NVEFWGk5lSNR6SuSbD1jzIamkH0UNUsvh5vULMOajIL0ueFGUDh56HexM0IpJALyWC+fzOOfW5QIyPO+9otAex4AceGOq+swBEHOufBFP9wCV2xXm1DzlOWB5bovTsCNZyll2S6n1M0uNd3XM+s7gTSO5OSzvSeI0BwkA9wopFSlyAY2n7wHeZOQ+9kElcaPpOQ+N88tSSAJ94GdzgCoFV+oJ/y3I2sru8XkhDSBRgiUoOAZo1pKfkvOBhI6BWfy3DAJqwg5cHcgAjWqQfhpxVQI6wk7VzAlwX4wErGLXYa3YcIv29G4Iy0EkSAIGIWPoHxxFxwiKHdKlC2bRg9Cp7QZUchzKNk20pEuhYPOcbLMoFuUpWbyUhbuM2VKiDopc5Ads1AmVjfmx+jkONSHixfSgm58k6SilqDgFm64E+XDTcLW2B1iLIGyZVMv1LJUn9uWTXM3UGvr+kBioFyFLHuGna6o5NS+kaHROpY6E34t/Q2I1D5Qpna6V7js5ccNgBcwRUu4V4495fEZ5KF5q/cMzL+vW3b93IF5+HcdvJKL7mf9A2KoW2D2C22Wm0365fg3+EMJzz4Jegu3f5n9Bvggxd+36M2wCurXX9eWpvsPCG1DyHNYFfqwgvzrthwVbLg0/hsHXiH9J36GLl5hDH0X1H8r/Scegyof+Rfmf+mAU/rfi8Zz4fsX5p/sfyPA+cb3e5hP9r8axu/viv4GwhDKfLyfpf1l/GROPsT2ill8YHyw4OyBx/ED+5/i/mWhSy3VDYYnHsNzPP4BMIdiHB9et54QvJxdP2mzEydOnDhxYpe4XP4HLjUAxWUkjNYAAAAASUVORK5CYII=)
physics-General
physics-
From the previous question in the reference frame attached to the center f inertia, the total kinetic energy of the two particles is
From the previous question in the reference frame attached to the center f inertia, the total kinetic energy of the two particles is
physics-General
physics-
A closed system consists of two particles of masses
and
which move at right angles to each other with velocities
and
. In the reference frame attached to the center of inertia, the magnitude of momentum of each particle is
A closed system consists of two particles of masses
and
which move at right angles to each other with velocities
and
. In the reference frame attached to the center of inertia, the magnitude of momentum of each particle is
physics-General
physics-
A man of mass m is standing on a platform of mass M kept on smooth ice. If the man starts moving on the platform with a speed v relative to the platform, with what velocity relative to the ice does the platform recoil?
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)
A man of mass m is standing on a platform of mass M kept on smooth ice. If the man starts moving on the platform with a speed v relative to the platform, with what velocity relative to the ice does the platform recoil?
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)
physics-General
physics-
A boy having a mass of M kg stands at one end A of a boat of length dm at rest. The boy walks to the other end B of the boat with a velocity u relative to the boat. What is the velocity of the boat? Friction exists between the feet of the boy and the surface of the boat. But the friction between the boat and the water surface may be neglected. Mass of the boat is 4 m
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)
A boy having a mass of M kg stands at one end A of a boat of length dm at rest. The boy walks to the other end B of the boat with a velocity u relative to the boat. What is the velocity of the boat? Friction exists between the feet of the boy and the surface of the boat. But the friction between the boat and the water surface may be neglected. Mass of the boat is 4 m
![](data:image/png;base64,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)
physics-General
physics-
A equilateral triangular, square and circular plates of same thickness and made up of different materials are arranged is shown in figure.
The ratio of their respective densities are
. The centre of mass of the arrangement lies
A equilateral triangular, square and circular plates of same thickness and made up of different materials are arranged is shown in figure.
The ratio of their respective densities are
. The centre of mass of the arrangement lies
physics-General
physics-
The centre of mass of a triangular lamina of uniform density of height h is
![](data:image/png;base64,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)
The centre of mass of a triangular lamina of uniform density of height h is
![](data:image/png;base64,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)
physics-General
physics-
A semi-circular plate of radius R has density
, where
is the distance from centre. The position of centre of mass from 0 is
![](data:image/png;base64,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)
A semi-circular plate of radius R has density
, where
is the distance from centre. The position of centre of mass from 0 is
![](data:image/png;base64,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)
physics-General
physics-
A semi-circular plate with cavity having inner radius R and outer radius 2R with uniform density is a shown. The centre of mass of the thin plate is at
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)
A semi-circular plate with cavity having inner radius R and outer radius 2R with uniform density is a shown. The centre of mass of the thin plate is at
![](data:image/png;base64,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)
physics-General
physics-
A rod AB of length 10 cm, has its mass per unit length varying from 1 kg/m cat end A ) to 2Kg/m ( at end B). The distance of centre of mass from end B is :
![](data:image/png;base64,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)
A rod AB of length 10 cm, has its mass per unit length varying from 1 kg/m cat end A ) to 2Kg/m ( at end B). The distance of centre of mass from end B is :
![](data:image/png;base64,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)
physics-General
physics-
If a square of side R/2 is removed from a uniform circular disc of radius R as shown in the figure, the shift in centre of mass is
![](data:image/png;base64,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)
If a square of side R/2 is removed from a uniform circular disc of radius R as shown in the figure, the shift in centre of mass is
![](data:image/png;base64,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)
physics-General