Physics-
General
Easy
Question
A block P of mass m is placed on a frictionless horizontal surface. Another block Q of same mass is kept on P and connected to the wall with the help of a spring of spring constant k as shown in the figure.
is the coefficient of friction between P and Q. The blocks move together performing SHM of amplitude A. The maximum value of the friction force between P and Q is
![](data:image/png;base64,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)
- Zero
The correct answer is: ![fraction numerator k A over denominator 2 end fraction](data:image/png;base64,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)
When two blocks performs simple harmonic motion together then at the extreme position ( at amplitude =A)Restoring force
Þ ![a equals fraction numerator K A over denominator 2 m end fraction](data:image/png;base64,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)
There will be no relative motion between P and Q if pseudo force on block P is less than or just equal to limiting friction between P and Q.
i.e.
Limiting friction
Maximum friction ![equals fraction numerator K A over denominator 2 end fraction](data:image/png;base64,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)
Related Questions to study
Physics-
What is the maximum value of the force F such that the block shown in the arrangement, does not move
![](data:image/png;base64,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)
What is the maximum value of the force F such that the block shown in the arrangement, does not move
![](data:image/png;base64,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)
Physics-General
Physics-
A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is
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)
A block of mass 0.1 kg is held against a wall by applying a horizontal force of 5 N on the block. If the coefficient of friction between the block and the wall is 0.5, the magnitude of the frictional force acting on the block is
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)
Physics-General
Physics-
A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle
to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
![](data:image/png;base64,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)
A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle
to the vertical. The block will remain in equilibrium, if the coefficient of friction between it and the surface is
![](data:image/png;base64,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)
Physics-General
Physics-
A 10 kg block is connected to an empty 1kg bucket by a cord running over a friction less pulley. The static friction coefficient is 0.4 and the kinetic friction between the table and block is 0.3. Sand is gradually added to the bucket until the system just begins to move. The mass of sand added to the bucket and the acceleration (in m/s2) of the system respectively ( g = acceleration due to gravity)
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)
A 10 kg block is connected to an empty 1kg bucket by a cord running over a friction less pulley. The static friction coefficient is 0.4 and the kinetic friction between the table and block is 0.3. Sand is gradually added to the bucket until the system just begins to move. The mass of sand added to the bucket and the acceleration (in m/s2) of the system respectively ( g = acceleration due to gravity)
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wGhOzXJ7oIss0xLdk3Wi+qfNuS1xcuXIgPPvgA69atQzKZBMuyMJvNOVd1J6K3txeKoug6t7SguBmGwRdffIGhoSG8/PLL9EtgWRZ2ux3RaBSKotCwTADjPAhELIIg0PrXJHkgkUiM8wLYbDZEIhH6xG82m8c9pJHsmXQ6jb/85S85b/dqm1XtNch+nzx4qS9E9XGIJ4NciNu2bcPhw4fPefDNPp+6PUmuB2y1Vyj7GOoxZNvk+YrmZ6P+bNnwPI9gMIg///nP2LdvH6LRKFwuFxYvXoxvfOMbRT0czps3DxzHlfcKpaIoqKurgyRJOHr0KB577DH6gchMrJ5piaDIe+ofnHgNyB2A1NImMzgJdiI/jNqlRtyBDMPg+uuvp68RyJjIxUNccOrjq707JpOJXliCIJzjtSEXVzKZBMMwNEGYHJ/8EQSB2uLquw65OMi4Sew4ieMm3wWZCNTjU3tMiJdEFEXqNs11gZFzkDQ24plRX3jAWDbO+vXrsWvXLpw9exZerxd79+7FnXfeWZS4STMsSZI07zPTaDJLGhoaEI/HUVdXhxtvvLHUYyoJ+bwVxeyfb5+pHC97li7kASnmeBMdY+3atXj66afh9/vzVvKaiO7ubsiyPKmE7ZlCs7dEi2ejHMjnjShm32LfK2YsWjwgxRwv3zFcLhfWrVuHt99+G+FwWPOYCeSOU11dXfS+M0XZJCsYTC8Mw6CpqQlXXXXVOLNMK0uXLgUwtvyuVzSLeyL3nfq17H+r983nIsw+j5bj59s/e6xTIft8sw3ycD6ZzxePx2lysl6ZclRgLnFO9O9cgpnoy813/EL7GwKfGEX5Xy2XyeDz+ehDs17R5Ap84YUX8OWXX+LYsWO4//77acIAwzDjvAcAxj3Nqz0Hag+K2hNAjkGe6ElwEYCcLi31e8R7oB6H2rMyUQEadQyIelu16zA7AEkd5KQ+rvoOku/hLJdPnGTIZ6+gqh8O1d+tulGs2uWXy+1J3JjqOJfsfcmqa1NTU9EXb0VFBc2k1yuaZm6Px4NkMolbbrkFH3zwAe644w7Y7XYMDw/j5MmTcLvdiEQicLlcaG1tBcdxkCQJp0+fhsViAcMwNNDf5XJhdHSUCioUCsHn8+H06dPwer3o6OhARUUFzGYzXZAhq2nENiR+c+KOSiQS1C1H3GxWq5W6qiwWC1iWpTU5yI9tsVjouH0+H139NJlMdAyKMhY2GggE0NXVRQvdELclWUSSJAmhUIi2BzSZTDSHc2RkBKOjo2hpaUEmk6HFcCoqKjA4OIhAIACXy0Wz+4koSaVau90Os9mMQCCAWCwGAHThrLKyEslkkroVbTYbotEodu7cicWLF+Omm27Km71EFrRI4nQxmM1mpNNpjIyMwOPxFLXvTFFQ3JlMBldccQUYhsGuXbsQiUTwrW99CwDQ39+Pnp4etLS0wGQyweVy0cUbQRDg9/sRiURQXV2NVCpFKyqRmZqE0iaTSfh8PkQiESxduhSVlZUQRZHOPuofh8w+VquVztBE3Gp/Oik3oC5LlkwmkUgkYLVaIcsyrevBMAyGhoYQDAbBMAzsdju8Xi9d1bTb7TQhtrKykuZpklmS+JVJWDCpD+JyuWCxWBCLxRAMBmG322liBBkvuQsIgkBXgoEx8TqdThr+KwgCotEo+vr6aIUqURRhs9nAMGO96kOhEK06NTQ0hMWLF+PrX/96QRFMxtMTCoWQSCRw+vTp8hU3Waomtz+r1UpjrRsbG+kStdq0IDOCx+OB0+mkP8TChQthMpmoScBxHGpra8GyLObNm0crK5FaeeSWnZ0po17aJyubarOIYRi6DQkOYpixAj3k/GSWJ7fy6upqmuxKjqtOPDaZTKivr6dpZuo4amKyeL1euFwu+h2ox09Wb7PT1NQmTbb9q/Zbk99h/vz555hC5N8ul4uWQZs7d+64hZzphpg7ek6702SWqGcY8kWq20hnb0sgMyZBnQ1C9h83mP8vpuxM81y3zHy2ePaydfZ72XEr6nNkn0e9Dcdx45IVch0j+/Oqt5uoSI56/1z7qrfJ175Effx89V2mE6/XC7PZDK/XW9LzTAXDzz3LIKIudYOqcDhMHQB6xRD3LIQEspUSn883qWX7mcQQ9yyD2OgVFRUlDZMg5lfZx5bks99KbddNJiCpFOfNFdw00TZaj19MQJT6/xNBjhuNRlFZWalpPJNh0aJFEARB181nNXlLBgcHx2W2HDlyhHohSCaLIAhwu910WZb4Y5PJJPX38jxPY7pJSV1SNkIQBPh8PjQ1NSEQCMBms9GwVJ7nEY/HYbFYqF91dHQUDodjXIY8+VtRFDidTgwODsLtdiMYDNJkBlJknbgiyTnVWfVOpxO9vb2oqalBNBqFKIo0XJXnecRiMVRVVcHv98NsNiMajaKurg4+n4+WLOY4DpWVlQgGg3C73RgYGEBNTQ1dyOrv76f/JwIJh8NwOBwYHh4GMPaQ6/F4MDIygkQigebmZrjd7oIruplMhiYilIozZ85Qr5Ze0TRzE3+u0+nE559/jh/84Ac5tyOzBtkn+z3yei6PBvl/rsxv9X4TzXrZXodc+6jfB5AzozzXvrk+qzr7W70CmP19aJ3ps8cJjJWRi8fjCAQC6Ovr07Tcnclk4PV68dvf/rbgtpOFxKVMNV2tlGhKViB5ci0tLbjppptKPiiD/9Hb24uBgQG8/fbbePHFF7F27doJBc4wDE6dOgWbzYYbbrihZONyOp3gef4c96ie0DxzG5w/yDL/6tWr8cQTTxQsp7B79278/ve/L6lZQprUkhVoPWJ4S3QOaQ2ibhgF/M9UzP5DmEr/IC2QPj967s9piLsMILmm6sjEQqiX50tBKpWiSeJ6xRC3zjGbzbBYLMhkMhgcHNScEiZJUkmTd51OJ8xm84Tli9UxMKW+2HJhiFvnkLgWlmVRV1cHt9tdcB9SjqKUPmgS4Jav43I+ZlLghrh1DnEFKspYH02trQUTiQQSiUTJxkUKIkUikZKdY6oY4tY5JGSW5/lxD5SFUDe7mi5I7PzevXvxxz/+Eel0msbq65Gy6axwoULa4pF221pu62RharpcgZlMBqOjozh+/Dj279+PEydOgGEYRCIRPPHEE1i7di0uvvhiVFVVaTKF8i3iTTeGuHUOyZskqWdaIClnJCwCKM7WVYuOdAresWMHfD4fvF4v7el5/PhxiKKIw4cPY+/evfjqV7+KSy65BABomt35TKw2xF0GBINBWkMxX7JCNupE7WIh5e4EQcDRo0exdetWtLe34ytf+Qqamppw6NAhKIqCe+65BzfeeCMYhsGRI0dw8OBByLKM1tZW2Gw2OJ3OCRMnskMNphtD3DqH9LNX1zwsBAk2m6xZEgqFkEwmUV1djWAwiP7+fvz4xz+m6YbLly/H4OAg5s2bR/vKNzY2oqmpCTt37oQoirjooos0jbWUAjfErWNIIFV1dTVNLtYaP52dA6r1fMBYrLYgCDhz5gx2796NBx98EHa7nb7vcDggiiJ4nqezMsdxWLx4MXiex9atW+FyuTSXfSiVDW54S3SO2WyGzWYDx3GavRKkUmwx4ajpdBqxWIyWhwgEAnjiiSdw++2347LLLjtne0EQctaCaW9vB8/z+OKLL+h4tYp2uu1zQ9w6h3hLANDyz4UgicrFzNykCD2pYvDII4/g7rvv1mxeEHiex913340vvvgC77zzTtEZ+NMpcEPcOoYsWZMWheRBTwvq8sJasn1IcX+WZbFjxw60tbVhwYIFkxJbXV0dNm3ahA8++ABvvPFG0WbHdAncELfOSaVSdOa2Wq2aGpqSalRa7HPSS5I82CUSCbzxxhtYs2YNKisrJ12auaamBg8//DB27tyJd999d8Z822oMcescskJJ2q9oaWqqrnWo9fgMM9Y94pVXXkF7ezvWrFkzpXErylhHjo6ODnR2do5bps8Ozy0Vhrh1Dqmepa5BWAhS4k1r4BSxsw8dOoRjx47h+uuvn7bs+U2bNkEURbz00ksznpJmiFvHkIhAURTBsiz1ZhSCJD9rXcRRFAXBYBAnTpxAe3s7nE7ntAib5MR+97vfxfbt2/Hll18Wlck/VQxx6xgiBFIMtJjSEaRKrtbtT506hTNnzmDlypXT2hVYUcbaiN96663YvXs3uru7p+3YhTDErXPS6TSCwSAkSYLdbteUiaM15JXMnIlEAp2dnWhsbERzc/O0jFsNx3G49tpr0dLSgrfeegunTp06ZwylwBC3ziF1WXieh8lk0jwb8zw/4bbqEhwnTpyA3+/HypUrS5bNLooirrzySrAsi927dxfcfjrcgYa4dQ5x68myjGAwqDkhlxQnKoSiKPjvf/8LAFi4cOGUxloIh8OB1atXY2BgAJ2dnSU9F2DElugenudhtVrpTKzFLCHeEi0rlIcPH8a+ffvwox/9qKj+NvkKIhXioosuQjQaxRtvvAGHw4H29nbN5ywWQ9w6h/i1zWYzQqEQIpGIpoUcoHD9QlmW0d/fD7vdDpfLdc772f10JEmi/vP+/n7a0cLtdsPlctFtC12EVVVVYFkWIyMjtPRcKTDErXNIwH8mk6F1GQvBMAzt/zPR7H3y5Em8/PLLeOqpp2hJOWLOhEIhBIPBcX19PvroI4yOjiKVSuHIkSNIJBKIxWJoa2tDY2MjeJ6H2WzGkiVL0NLSAlEU6V1HXTy/ra0N119/Pd588004HA4sWrQob8m6qTxwGuLWOWT2zWQymDdvHi1tV4hC8dzDw8P4+OOPsXbtWoiiCEVRaJCWLMsIhULYu3cvJEnCyZMn6VjIgs9Pf/pTNDc3I5lM4qOPPsKOHTvoA+zJkychiiIaGxuxfPly1NbW0gZcdrsdmUwGS5cuxcGDB7Fz5040NTXlrX8ylQdLQ9w6R1EUepsnzbQKQQKsstsVqtm6dStGR0dx//33085kpK1KV1cXBgYGcPToUciyDLvdjpqaGnzta19DU1PTuONYLBZs2LABGzZsgKIoSCaTOHDgAE6cOIF4PI4XXngBixYtQnNzM5YvX45UKoVwOAyLxYK1a9fimWeeQV9fHzo6Oqbl+1JjiFvHkFmbJAXEYjHN4iZlonNx7NgxHDp0CLfeeisSiQSCwSB4nkcwGMT27dsxPDwMjuOwatUquN1uLFiwADabTXM2/SWXXIJLL70Uw8PDOHbsGE6cOIE9e/bg888/x+LFi3HxxRdDURQ0NDRg0aJFeOWVV/D9739/0g1f82GIW+eQXpgANIu7UOb7Rx99BJfLhXnz5qG7uxscx2Hfvn3o7OzE/PnzceWVV2LevHloaGig9rKWlDWGYcaNt6amBvX19Vi6dCkGBwfR2dmJjz76CNu3b8cdd9yBhQsX4pZbbsGOHTvwi1/8Ag899BAaGho0fjOFMcStY8hs7ff7iypsqe7aBoz3eiiKgiVLlqC1tRVWqxXRaBRPPfUUVq9eje985ztoaWmhzV0JxeRiqm1kcj6v14uqqiq0tLTA5/Ph008/xZNPPomOjg5s3LgRV111FX7xi1/Q/qbThSFunUNKqTEMg2AwiGQyWbD4JMuyiMfjkCQJHMehs7MT4XAYtbW1eO655yBJEn74wx/iBz/4AaLRKJ5++ml4vV5YrdaSlWJgGAY2mw02mw1z5szB+vXr8corr+C2227DL3/5Szz44IN48skn8Zvf/IZ6WKY6FmOFUueo+7U3NjZqWh4nXYdJ1rwgCOju7sarr76KAwcOoL6+HldddRUefPBBvPTSS2hubqadiKeKlrsLz/NwOp247777cOjQIbz22mt46aWXUFtbi02bNtGWJFON+zZm7jKAxHTHYjFIklSway8JeSUPpHPmzMHx48dhtVqxYsUKVFdX4/PPP5+SeKYrJBYANm/ejFAohEceeQSXX345HA4HBEGY8jkMcescYpKk0+mi2uKp+/BYLBYsX74ckUgEl156KVpaWug22eQS1GRFVkyIrsPhwK9+9St60U0HhlmicxRFQSAQQDQaLaezWwMAAAqcSURBVCpBOJlM0txLlmVhsViwefNmbNmyZcK63blqak/GXClmn0wmg3feeQcvvPAC9u7di6qqqmkRuCFunUOCoEh7Qa2Qbgzk3wzDoLe3F0eOHKEhp8UIqJhzFzNjA8A//vEPPPLII+js7MTAwIDm8xTCMEt0DsMwtA9msQInkAc4l8uFqqoqHDt2DG+99RbuvfdeLFiwABaLRdNxC2Wwax1bOp2GJEn4+OOPsW3bNtTX12Pjxo0YHR3Fxo0bp80sMcStc8xmM6xWKxRFgdVq1ZwgnB1bYrPZcN9992HLli3o6OjAwoUL8eKLL4JhGNx2221obGyEx+PRNKapeFVIcsTzzz8Pm82G1atXY8mSJQgEAnjsscewevVqQ9wXCrFYDENDQzSYSWtxSWJzkyVzjuPQ1taGoaEhVFdXQxRF1NbWwu/345lnnkFraytWrVqF5cuXw+l0luSzDA8PY9euXejp6cGqVatw2WWXwW63027Hk61Kmw9D3DqHYRi6IBMMBovqYpBvZdFqtaK9vR1nz55FTU0Nfv3rX2Pbtm14+eWXsW3bNlx77bVYvXp10YU08yHLMp577jl0dXUhkUjguuuuw/r16+kzQTqdxr///W/ceOON03I+gvFAqWOIeTF37lw4HA7MmTNHc3BRrlqBNTU1uOaaa7BlyxawLIu5c+eirq4Odrsdd9xxBx577DEsXLgQr776Ku68806cPXsW8Xh8Um1BSPWqrVu34tZbb8XAwAAuvfRS/N///R+uvvrqcWOz2+149tln8cADD0xrwrAxc+sYsnhDvB3E562FeDyOeDxOLwZFUWCxWLBs2TL89re/peGwDMPAZDLREmjf/OY30dXVhd7eXjz66KMIh8O4/PLLceedd9Il+okIBoMYGRnB4OAgnn76aSxYsADf+973sHLlyrwZRP39/bQj8XRiiFvnkGpTxRbasVqtsFgs57xOOqIdOXIEy5cvBzDe+6EoCtra2tDW1ob29nZIkoR9+/bhl7/8JdatW4fGxsYJL7DPPvsMe/fuhdvtxo9+9CPMnTs3Z3tB9Tk3bdqEp59+mmYDTReGuHVOMpnE6dOnEY1G4ff7kUwmCy6/k3Sx7PxERVGwbNkyXHHFFXjppZeouHPtDwCNjY1QFAUtLS1Ys2YNXn31VWzdujWvLZ7JZHDFFVfgd7/7HU1P0xJRODQ0BK/XW3C7YjHEXQaQmXui/jK59smXeFtdXY0jR44gGAxOWDqNvM6yLObMmYMHH3xwch9gAkZGRlBdXV2SJGHjgVLnkN6P5G8tjVMZhoEkSXmX6tetWwdJknDgwAFNY5iqqUACtNR/yDj/+te/4uabb6b9dqYTQ9w6h+d5uoJosVg0p3qROPBsFEXB3LlzIYoiurq6NI8jl0C1/pnoeJ9++ikWLFhQklbehrh1jiAI8Hg8sFgsNDa7EFqiCAVBQDgcLqrA5nTz2muvobm5GfPnzy/J8Q1x6xhFUaiHhOM4Wu21EJlMpmCV18cffxyHDx/G8ePHp3PImslkMti3bx/q6+vhdrtLUhDTELeOIbmQqVQK8Xgc/f396O3tLSgE0ro6FovlfJ/kNcZiMfh8vhlt5UHOn06n6YNyqe4chrh1jizLNOu9sbERc+fO1SQGURRz+rkJDMOgvb0dhw8fPi+mSSAQgNlsRm1trSHuCxXS953UL9FawrjQjMhxHO6//35aIm0mYVmWVrNatWpVyWoFGuLWOWRlknQn05pqRhZxJkIQBFRWVqK7u3tGTRN1WbZSYohb56j93MFgcFxXsInQ0kG4srISV155JbZv3z6p4KjJMjIygqGhITQ1NRVcbZ0Khrh1DsuycDgcNAtHaxiqllreoiiitbUVfX19mloAThf9/f3o6enBokWLpr2EmhpD3DqHVHgl3gVSI7sQ6uashY5PGq3OBKTOtyzLtEtbqTDErXNEUURFRQUYhqGRflpsVRJNWIglS5bg8ssvx7/+9a/pGG5BRkZGsGvXLqxcubJkizcEQ9w6JxKJIBQKUX+31kRerQV3LBYLHA4HgsHgdAxXE/F4XHPD2KlgiFvnMAwDn8+HkZER9Pb2IhAIaNpPywMlwePxwOfz4cSJE1MZqibS6bTmu8pUMcStcwRBQF1dHWw2GxoaGjRlqJOC9Vp84izLoqWlBaFQCAcOHJj2JF1gTNDENXn8+HGYzeaSFJvPxojnLhN4nkc8Hkc0GtWUnU4eQrUI3G63Y+7cuTh9+jR27Ngx6foo+RgdHaVRje+++y4URSlZhr0aQ9w6h3hLUqkUPB6P5tbVJpNJs03r9XqxceNGvP7669i2bZvmVVCtRKNRsCwLs9mMaDQKt9sNn8+HysrKaT1PNoa4dY66kLwsy4jH4wXrcwOgzZu0xH+Tmibf/va3J6wjOFkSiQT1u5PPU6pOxWoMcescnudRVVUFq9WKSCRCM+ELeUIm6omTC5ZlS2YqkM4OM43xQKlzEokEBgYGIEkS4vE4bWxaiGQyqSklbSYgJSRmWuCGuMuETCYDm82mOUnYbDZrTkmbSWZS4IZZUgaoM9m11gokEYRaTJPpjAgsZpGp1Bgzt86xWCywWq2QZRkWi0VTOw0SUjoTCyW5zq2FmZjBDXHrnHg8jlgsBkEQ0Nvbi2g0WnRx95nmfJ03G0PcOkcURZhMJhrhp0XYiqIUTBAuNXoQuCFunUMybziOg9Pp1FxPjyx5n0/Ot8ANcesclmUhCAL9W4tgyaqmHjifAjfEXQaQWtuhUEizv1hrssJMcL4Ebohb54iiSHviFLM0Xkym/GzF8HPrnFAohOHhYQBjTZuKce+db5tXzfkYizFz6xyz2YxEIoFwOIzu7m709/cX3IdhGM0VYWczhrh1jizLtMXH4sWL0dTUVHCfTCYDu91e0szycsAQt84hLj2O4+Dz+TA4OKipVqC6PfaFiiFunSOKIqqrqyEIApxOJ8xmsyb79Xwtv+sJQ9w6R11xanR0FPF4XJMrsJgE4dmKIW6dw3EcLBYLWJaF1Wotqg/lhe4KNMStc1KpFK2zTfzcWmZuSZJKkjJWThjiLiMqKio0p4IVm2Y2GzHErXOSySTC4TAymQxCoRACgYAmb4ksy4a35HwPwGBibDYbBEFAMBiEzWZDJpPR5C1hWbakRSbLgQv705cBsVgMqVQKFRUVtJxxIdGSeO5S1+LTO4a4dQ7HcUgmk7Qgpt/vL5t47vONIW6dw3Ec3G437HY7OI7TXL0VmNlMcz1iiFvnWK1WeDwecBxXlJlBMnb0FBk40xji1jnE42EymRCPxzU1SlIU5bwUwdEbhrh1DmmYGg6H6UOlFlegIXBD3LpHFEXY7XYqaC0VpxRFoTUFL2Qu7CWsMoAU4RkZGQEw1kaEzMr5ICGvpEnUhYohbp1DPCR+vx8tLS2oqqoqGDMiSRLMZvMFLWzAELfuURQF9fX1uPLKK7F582Z8/vnnExa4ZBgGgUAAK1asQDKZ1GUxzJnCEHcZwPM87rrrLng8Hlx00UWYO3fuhA+V6XQaqVRKcyvt2QqjXMiOUINZjeEtMZi1GOI2mLUY4jaYtRjiNpi1GOI2mLUY4jaYtRjiNpi1GOI2mLUY4jaYtRjiNpi1GOI2mLX8P6hSC4LhF15MAAAAAElFTkSuQmCC)
Physics-General
Physics-
A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is
, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank
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)
A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is
, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank
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)
Physics-General
Physics-
Initial velocity of the block
while external force on it is
. It coefficient of static and kinetic friction are .3 and .2 respectively then distance traveled by the block in 12 sec. (g = 10 m/s2) is:
![](data:image/png;base64,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)
Initial velocity of the block
while external force on it is
. It coefficient of static and kinetic friction are .3 and .2 respectively then distance traveled by the block in 12 sec. (g = 10 m/s2) is:
![](data:image/png;base64,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)
Physics-General
Physics-
In the system shown, the acceleration of the wedge of mass 5M is (there is no friction anywhere)
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)
In the system shown, the acceleration of the wedge of mass 5M is (there is no friction anywhere)
![](data:image/png;base64,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)
Physics-General
Physics-
A particle starts at ‘A’ with initial speed
. It moves along a circular path under the action of a variable
![](data:image/png;base64,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)
force which is always directed towards ‘B”. A and B are end points of a diameter. When it reaches the point ‘P’ as shown , the speed is (Neglect the effect of gravity).
A particle starts at ‘A’ with initial speed
. It moves along a circular path under the action of a variable
![](data:image/png;base64,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)
force which is always directed towards ‘B”. A and B are end points of a diameter. When it reaches the point ‘P’ as shown , the speed is (Neglect the effect of gravity).
Physics-General
Physics-
A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration
in a direction forming an angle
with the horizontal plane. The acceleration of bead with respect to rod is
![](data:image/png;base64,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)
A bead of mass m is fitted on a rod and can move on it without friction. Initially the bead is at the middle of the rod and the rod moves translationally in a vertical plane with an acceleration
in a direction forming an angle
with the horizontal plane. The acceleration of bead with respect to rod is
![](data:image/png;base64,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)
Physics-General
Physics-
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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)
A lens when placed on a plane mirror then object needle and its image coincide at 15 cm. The focal length of the lens is
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)
Physics-General
Physics-
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
A thin rod of
length is kept along the axis of a concave mirror of
focal length such that its image is real and magnified and one end touches the rod. Its magnification will be
![](data:image/png;base64,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)
Physics-General
Physics-
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,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)
A ray of light makes an angle of 10o with the horizontal above it and strikes a plane mirror which is inclined at an angle
to the horizontal. The angle q for which the reflected ray becomes vertical is
![](data:image/png;base64,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)
Physics-General
Physics-
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
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)
PQR is a right angled prism with other angles as 60o and 30o. Refractive index of prism is 1.5. PQ has a thin layer of liquid. Light falls normally on the face PR. For total internal reflection, maximum refractive index of liquid is
![](data:image/png;base64,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)
Physics-General
Physics-
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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WVNvMfLRaLQ2WO5+fnk5aWxsKFC9FoNIwcORI/Pz+bNUGtoaqqir1793L8+HHgbs+huXPn4uXl1RZmA0KQLcLFxQWtVktZWZnNNaPZbLZ5itPRFBUVsX37ds6cOUNwcDC1tbW4urq2SZuV0tJS/vKXv3D9+nXGjh2Lq6srW7ZsIS4ujqeeeqrNEpWFIFuAu7s7jz32GHv27EGn01ll/jjKxkav1wMwb948wsPD2+xI02g0snv3brKysnjrrbeIjo7GycmJmJgYPD0923T9LATZAlQqFb169cJkMlFUVGR1bGavjU11dTUHDx4EYNSoUYSGhrJw4ULUanWbllbodDo2bdrElClTmly/3B4nOGJT00L8/Pyora3lxIkTNk9nOtJLSpJETk4OCxYs4OOPP8bT0xOlUomTkxMajabN63zy8/MpKipi4MCB7V5DJDxkC+nZsyd9+vRBr9db7aolSWr3nbYkSU2qH52dnZk4cSLPPPNMu99zU1RUhFKpxMfHp13HAeEhW4y/vz9RUVGUlpZSVVVl9by9PKTFYqG0tJSsrCzWrFnDv//9b2QyGWFhYUyePLlDLl1yc3NDkqQmXS/y8vKorKxs87GEh2whCoWCoKAgDh06RElJiVU8r6EYqq3DP/X19aSkpHDo0CH69u1LTExMm76/JSQkJPD444/z+uuvN/YHOnr0KLNnz25sB9hWCEG2gpCQEEwmE9evX7dqQ9JWgpQkCZ1Ox/Xr19FoNISGhtKvXz8GDhxIRESEXe7fdnNz4/XXX+fdd98lIyMDgAkTJvDYY4+1+VgyqavkT3UAJSUl/Pa3v8XNzY0FCxbg6+uLSqVCqVQ23lOjVqsfabd95swZvvjiCxQKBePHj7eLR7QnYg3ZCnx9fYmPj+fixYvcvn27yTOLxYLZbH6ktaQkSfznP//B39+f5ORkIiIiHtXkTocQZCuQy+XEx8ej0+m4ceNG485akqTGnXZri+gvX77MBx980NiMIDk5mRkzZhAXF9ctS2/FGrKVxMTE4O/vz4kTJxg8eDBqtbpJyMdkMjXGBL+PmzdvsmXLFo4cOdJkY+DoyQ/tjfCQrcTd3Z0xY8aQkpLSGP5p8JCSJGEymVpUGqrX69Fqtbz66qusWrXKZt+g7ojwkA/B4MGDcXV15dq1azY7hd3vJc1mMzqdjmPHjlFSUsKsWbMIDw/vcpcetQXCQz4EMTExJCYmsnHjxsaGTPd+jEZjk7XkjRs3+POf/8zmzZsJCAjoNhdpPgxCkA/JpEmTOHfuHGfOnMFisTT5NHQLq6qqwmw24+LiQlJSEv/85z8ZM2ZMh5yudFZEHPIhqaurY+LEiSiVSjZs2GAV7jEYDBgMBkJDQ3F2draTlZ0P4SEfEmdnZ1544QUOHjzI2bNnrbykSqXC3d2903bYtRfCQz4CJpOJp59+GmdnZz788EOruKFMJsPDw8PmZUsC24j/vo9AXl4eOp2OjIwMsrKybK4l27vjbFdDeMiHID8/n08++YTMzExiYmI4efIkZrOZrVu3NmlbB/9rVuXt7W0nazsXIg7ZCm7evMnevXvZtGkTgwYNYu3atYSGhnL58mWefPJJNm3axNSpU63+XHV1Na6urmJz0wKEIJuh4RaGo0ePsmnTJry8vPjwww8ZMGBAYypYaGgov/jFL9i9ezfDhw/Hz8+vyTskSaK4uJjg4GCHbSjgKIgp+wFYLBZKSkrIy8tj+/bt1NXV8fOf/5xBgwbZrObLz89n+vTpJCUlsWTJEptn2W5ubvj6+oqd9/cgPOR9mM1mrl+/zsWLF9m3bx9lZWVMmzaNUaNGfW9AOygoiPnz57N582ZOnz5NXFycVZ2NTqfD2dkZd3d34SkfgBDk/2M2myksLOTkyZMcOXIEnU7HqFGjGDNmTIs2JGq1mlGjRnHw4EH27NlDSEgIHh4eTSoULRYL5eXlKBQKXF1d2/Ov02npVlO20WhEqVQ28U4Nl2sePXqU48ePYzabiYqKYvTo0a2+Ys1isZCWlsYbb7xBcnIyycnJVh0tZDIZGo0GPz8/cYRog27jISsqKiguLiY0NLRRCFVVVWRlZZGamopMJiMmJobBgwcTFhb2ULUrcrmcIUOGMG7cONLS0ggJCWHAgAFWa0a9Xk9paSlarVbsvO+jWwjSaDSyf/9++vbt2+ixsrOzWb9+PS4uLgwbNoyoqCh69+79yO1H3NzcmDVrFlevXmXjxo28/PLLNqfuqqoq5HI5Wq3WIfoCOQrdYso+evQoe/bsYdasWQC8/fbbmEwmJk2axKBBg+jZs2ebX+2Rm5vLnDlz6N27Ny+99JLN7zg5OaHVavH19XWo7mn2pMsL8sKFC/z+97+nvLy8MUA9Z84cJk2ahEajabeyUkmSOHDgAPPnz2f16tVER0fbLABruBjez89PhIPo4lN2RUUFO3fuJCUlBYvFQmJiIm+88QZJSUnt7pFkMhmjR49m4sSJzJs3j3379tksU2jY3UuS1O3raaCLJlcYDAYuX77MO++8w8aNG/H29kar1aJSqUhNTeX8+fMd1vX2nXfeYebMmTz//PONwrP1KS4uxmg0dohNjkyXmrLNZjNXr14lPT2d7777jsrKSp588kn69OljNTXHxsZ2WGGVXq9n4cKFZGdns2rVKkJCQppM30qlktDQ0A5p5uTodAlB1tfXk5+fz5kzZ/jvf/+LwWBg0qRJJCYmOkxYpbKykhdeeIHc3Fx+/etf07t3b4xGI87OzgQEBODv7y/WkHRyQZrNZvLy8jh+/Di5ublIksTIkSMZPny4wwWdJUkiLy+PP/zhD9TW1rJs2TK0Wi0+Pj4EBATYpWePI+Lwgrx16xY5OTlN8gwbGjJdvXqVgoICvL29SUpKIjExEV9fX4c9JzabzWRnZ5Oamsq4ceMIDw/HxcWlS98m21ocXpB37tyhoKCAgwcPkp6eztmzZxvbJ8fHxzNlyhQGDhyIv79/p4jlmUwmdDodPXr0EAFxGzj8POHu7k5kZCTXrl1j06ZNXLhwAQ8PD+bOncvSpUsJDAzsVP+wSqWyTa/R6Go4vIeEuy3qli9fTmFhIS4uLvTp04f169dbJcIKOj8Ou62TJIlLly4xe/ZsFi9ezC9/+UsyMzNRKBS8+eabQoxdFIfykJIkUVNTQ0FBAdu3byc7O5uf/OQnPPfcc3h6erJnzx70ej3Tp0+3t6mCdsJhBFlVVUVBQQH79+8nKyuL/v37M2XKFPr3798YEjl58iTx8fF2tlTQnthdkNXV1RQUFLBv3z4uXbqEt7c3kyZNIiYmRoRDuiF2E6TBYCAnJ4dDhw5RUVGBxWJh/PjxxMXFOczpiqDj6XBBms1mcnNzSUtLo7i4GF9fX4YMGSKEKAA6UJAWi4WCggJ2797NjRs36N27NwkJCcTGxuLm5tYRJgg6AR0iyIqKCrZu3cqxY8eIjIxk7NixRERE4OHhIRIKBE1oV0HqdDq2bNnC119/jbe3N4sWLWLAgAG4ubkJIQps0i5HhzU1NRw+fJjVq1ejVqt59913iYqKwsnJyWETHwSOQbt4yJSUFD799FN+9rOfMXz4cOENBS3G7nFIgeBehOsSOBRCkAKHQghS4FAIQQocCiFIgUMhBClwKIQgBQ6FEKTAoRCCFDgUQpACh0IIUuBQCEEKHAohSIFD8X9/li2J4PU/8gAAAABJRU5ErkJggg==)
A convergent beam of light is incident on a convex mirror so as to converge to a distance 12 cm from the pole of the mirror. An inverted image of the same size is formed coincident with the virtual object. What is the focal length of the mirror
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)
Physics-General
Physics-
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is
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)
Physics-General