Question
A smooth block is released at rest on a incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is-
The correct answer is: ![mu subscript straight k equals 1 minus 1 over straight n squared](data:image/png;base64,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)
Related Questions to study
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-
A block is kept on a friction less inclined surface with angle of inclination . The incline is given an acceleration a to keep the block stationary. Then a is equal to-
If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by
, then ![c o s blank B equals](data:image/png;base64,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)
If the sides a, b, c of a triangle are in G.P. and largest angle exceeds the smallest by
, then ![c o s blank B equals](data:image/png;base64,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)
Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of
at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
![](data:image/png;base64,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)
Two plane mirrors. A and B are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of
at a point just inside one end of A. The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (including the first one) before it emerges out is
![](data:image/png;base64,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)
A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is
![](data:image/png;base64,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)
A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source in the mirror is
![](data:image/png;base64,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)
Figure shows a glowing mercury tube. The illuminances at point A, B and C are related as
![](data:image/png;base64,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)
Figure shows a glowing mercury tube. The illuminances at point A, B and C are related as
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAQ0AAAB3CAYAAAAZ3BUbAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABa0SURBVHhe7Z0JtFVjG8ffkDlkjKRQaZSEkqJJiMxRxlokY4YMS4bUqpa0SmqRDCFUSGQIEUnGkiZjJClTFyFUhu/ze9q7brdz79n7DPues8//t9Zedc+w7737nve/n+l9ngr/+w8nhChYVq5a4/0vGJt4/wohRCDStjR4+8qVK11RUZFbvny5+/vvv71nhBC5wLbbbut22WUXV7lyZbflllt6j64nrKWRtmj8+++/bv78+XYsWbLE/fXXX94zQohcYIcddnC1atVyDRs2dNWqVfMeXU/k7sk///zjFixY4BYvXizBECIHWbFihVu4cKFbunSp90h6pC0aGCqLFi0y8RBC5CYIByGETKBAaMyoUKGC23TTTd1mm21W7scmm+jjFUfSjmmsWbPGDRo0yGIbxdliiy3sgyOiBcEg8IXll+afNi34OQiKr169WlZoObBq1aqNrvuBBx7oOnbs6H21nsgDoaWJxgknnOAOOOAA7ysRJZ988ombPXu2+/XXX8tFOBCM6tWru/3339/tvvvu3qMiSh566CGLMxYnU6Ih+zGGECknSo61FzUIxvbbb+/22Wcft9tuu3mPijgh0YghLFzu8jvuuGO5xBVq165toqWYRjzRXzWmVKpUydWrV8/ttNNOkS1exKo8rRwRDRKNmIJQ7LXXXhZbQECyLRycf9ddd3U1a9a0YiKyOCKeSDRiDHd7XIUqVaqYFZBNNt98c1enTh0TDmXN4o1EI+b4Qcmdd945a3d/zrvvvvu6qlWryi0pACQaBQCWxt57720Ckmk3BcEgS4JFs/XWW3uPijgj0SgA2NlIbIMjk5YAAoRQNGjQwAKu2XaBRG4g0SgQCE7WqFHDtkhnCkQC1wcxqlixoveoiDsSjQICwWCRk01JF6wM+jM0atRIglFgSDQKCBb3nnvu6erXr29ZjnQOysMbN25s+1yUXi0stPdEiBiivSdCiJxBoiGECIVEQwgRComGECIUEg0hRCgkGkKIUEg0hBChkGgIIUIh0RBChEKiIYQIhURDCBEKiYYQIhQSDSFEKHJulyvn+fPPP90ff/xhU+hLnleIQoAGR3RZ22abbaxpc9j2A9nc5ZpTosE5vvnmG/fMM8+4CRMmuLlz59poQbWRE3GHZcjsW3850ne1ZcuW7rzzznPNmjVz2223XSjhKBjRmDNnjhs4cKB744037GsavRxxxBGubdu21vhFiDjCoOYvv/zS9e/f3xUVFZk4cKNkFATWRu/evd3JJ59sjaGDUhCiwdDim266yX377bfupJNOcgcddJCbN2+eWR2YaJdccokN4hEibixatMhulvPnz3dNmjRx559/vrkkjz32mN1AGa/Zt29fd/zxx3vvSE5BiMZll11mF4pfijmkdLkmrrFgwQL33HPPuRUrVrgBAwZ4rxYiHvAZf/XVV12/fv1c9+7d3YknnmgzaujB+tNPP7mpU6e6Bx54wLVv395deOGF1q4xCLEXDdR0+PDh7txzzzVXZKuttvKecW7VqlXu9ddfd6NHj3Zdu3Y1P0+IuPDhhx+6IUOGuGXLlrnx48dv1C2emyXuCQLQs2dPE5UgZFM0ciLl+sorr5h1Ubdu3Q0EA5jZsd9++9nz06dPN2tEh464HL/88ou5JwQ7ieERxyh+YHUceuihdnNeunSptyrKl5wQjY8//tjG+uG7JYKZHcQziHuUvKg6dOTzQcaE0gJiGQQ/Ex3cMFkDuDK5QNbcEy5GycdKA7OMdviMDkR969WrZ24IU8+B74ELc+2117r333/fHhMiDjz77LOWABg5cqRZFCxHLGoOXHP48ccf3bRp08wSad68uT2WjOXLl9vUu2rVqtmYCahVq5Z9j5JE7p4QsOEH4ZcpfmA1sNiDHFwoBAbF5evi+eri+K/ToSMuB/AvVoT/+ebzv3r1ahMNDlwY1gXP+Wsm2YGrz7o87LDD1h2Zyj6mbWlkgk6dOrnTTjvNIsSJctFctJdeesmNHTvWPf74496jQuQ/U6ZMcddff70VcV166aXeoxvy4osvumHDhrkOHTq4q666yns0c0SePckEN998swVAO3fubC5KSb766iv36KOPup9//tleK0RcePfddy3diit+7733ukRVn0OHDrWbJtnDbt26eY9mjrwUDfy1UaNGWcq1VatWljHxwUzDv7vnnntcly5dXIsWLbxnhMh/SLWOGTPGvfDCC+6RRx5xtWvX9p5ZC8WO11xzjZWRX3HFFVb0mGnyUjSAC4JYHHfcca5BgwZmebBx7aOPPnKTJk1y3333nevTp4/3aiHiA7UaBPmxsm+55ZZ1xV1Y1lgfb731lrvuuuvsppkN8lY0SLtiphH1pYCFbMrs2bPduHHj7Hl8PiaeCxE3Vq5cadnBO+64wzIdxC34l0pQNnD26NHDPv81atTw3pFZ8lY0AFMNE+3JJ5+0OAbRYjIqXFQhCgksDeIcvXr1ss1q7HrNFnktGn5KqWQfjRz6EYWIDISDXa7ULoXtpxGGvBYNIUT0hBUNtfsTQoRCoiGECIVEQwgRComGECIUEo0YQ+cn9i189tln3iPZ5YMPPnAzZsxwP/zwg/eIiCMSjRhC2poWAhTGTZ482appo4DCPBoqTZw40TrJ50r/B5FZlHKNEfwp2RFMdeHLL79si5bt0UcddVTg3pJlwbmpUKQhDL0dSoJo8H3fe+89qy9o2rSpff9ErxW5g+o0ChD+hGzso23czJkzrRHzHnvs4c4++2zXsGFDW8Al4T3s7cEKoS9lpUqVvGdK5/PPP7fu8HScOvXUU+17JAI3hcpezs0IisMPP9yqG2kWLXKPsKKx6S3skBF5CzMz6OzEPp377rvPvf3229bq/uKLL7a9OizwkiAYDKGaNWuWe/rpp21PA12eilcdEg/hdRUrVvQe+e8O89/z33//vZX5//7777bBij0SJasVsSwOOeQQEyt2KDPPhvNUrlxZwpGDrPn7H+9/wZBo5CksaGIXS5YsMcvirrvusgU8ePBgu7uXtjh5H3t5EBfaDfD1KaecspE1QsMjnivu1rDzmF6u1atXt/4muCr+juSSwsFjtG2sU6eO7eLk9WwN4L0ISCIxE+VDWNGQe5KHsPi402MpsBOSzX3sgjznnHO8VyTGFwxGQjCIh5b2DOZJ5JqwSerYY4+185aEdnS4KldffbW5HTRGYgIeeyUSwc/6zjvvmEixr+jyyy83S4RWCNncUyGCoTLyAoDdwDSipU0cFgXxA+IXycAlefjhh92tt95qQUp6mASJZZQEK4GxEmRncI2uvPJKszpKgwl5bdq0cSNGjDCxoL3jbbfdpuxKniLRyCMIXOKK0LAF94LFijtStWrVpHdsYhEMnKKhC0N3sCDSucvzXtwhrAe+Pz0gyJpgSSSC19NchlgLHbipHaEvLClhtT7ILxTTyBNwB+6++27LXjAHg9m23LWxFJItfoYL0wGKc3CXP/LII+3uXxa4L7Sew4UpDb4vLgaT9GhLR30GsQxEJFHGhtezzRtXhu7YBHH5nb7++msL2hIoFdGjQGjMwIQnw0FmhFgCQUuyIwQUWaDJwLJAMLBSGKzNPJkgLkkQ0fBBgGiPT+wCS4i2+8zbSCRMCAcDgOh5SfaFVvuffvqpNc7lZ6TZTDJBE5lFohEjWEzciUlbYlWw6JnERV0FCy8ZCAYzPXk9YoMABI1hhBEN4LwIBcJGgRel5ARJE42k8EEcsEpI+eLWMAiZto+kf6tUqeK9SmQbiUaeQ4aDOzbNlAlw8jVDsY8++mibkFW8U3tZ0N16woQJVoDFMG5/En9QwooGIByIANkdMju4HdRsIAKlQVAVUeN9VJpSEMZ7/QlhWCQiu0g08hjqLphXS3CR2gYW7THHHGMVlQQRk8UuANeA4CKxD8x/mjRTK0EsIQypiAYQHMV1Iv26YMECSwczbS9Zj0sEh5+XeAdZHgrCsDoQukyUwIvSkWjkIdyZubNinmNh0Lq+devWVqpNMVWioGJJsEiICfB+3Bne57+/eFVnUFIVDWCh45rwcyOCX3zxhVkMyfag4HIhLn4BGIKDi0ZaFzenLFdHpI5EI88g0MlsFwKImOUsLoZGIRosviDWBaLDwkIwpk6dagN1EAxM/iCxj0SkIxqAYCAc/D4sfKwG/s/PlAysFVwx3k9WhilkCAiuGe5WkGsigiPRyBNINxIsJFiJYHA3pvy7e/fuFlAMujAIPFJYhTuCW0L8A5fEH7iTKumKBhCvwLXAwkAY2R9DWhUXJJmY8bPzO5BdQSwQjoULF9pzfI2gpvP7ifVINPIArAsWAMN/OTDFqbto165dKFeCjAN7TxAMmu1goZx++ukJN5GFJROiAfwciAR1GLgq9Nsg8MmBqCT7OREIrA4qWKkzIbhLzIPfEXclFddLbIhEI4fBjSBewR2XzAh3X39HahCzvThshWcRUcNB/wwmjjPSMlN330yJhg+ZETawIXJsXiOlipgEmenB84hEs2bNzD2hiMx3d0jb4gql6oYJiUbOQmYEN+KJJ56wDz21CSx0XJKwd0vOheCwj4QMBRvHiIFkkkyLBrDAqR7F0mL/C24LIoA1EcQyQhDJsJBCpnfIgw8+6IqKikx8EBCEI8h5xIZINHIMshrELwhy9u7d2wJ67Cw966yzUhq1x7mwVFgwv/32m+1DOfjgg71nM0c2RAOwCpjTSw0G09CxQBCCoEFfwK1p3ry5ZYYI/r722mt2HuInEo7wSDRyDPzv22+/3d1///0Ws2BjF4smVV+ccmuqRKl9QIRYONlYJNkSDWBh46rUr1/fDRw40CwP4hZYC2FAJDp27GiuGtcXMSWInM25p3FEopEjEKSkhwQiwSKhhwS9OoOWgJeEhYVrQ9csROeiiy6yuEC2MgjZFA3g5yal2qhRI3PX2FTHgidjEhTEEvGleI0Dl42gMCLCz64gaTDCioaa8GQY3AfKp6nqnDdvnpV/c7AgUh3ki2AQOMXFwRXp0KGDxQOymXIsqwlPJqGCletEMyFclDPPPDMloeI81KqQwn7++edNMHADybqIslGP0HIEV4TiquHDh5vPfsYZZ7hWrVpZZoQPcaqCwS5V7qItWrRw7du3z7pgQLYtDR9/7wkpWdLQCCPiQVVoGDiPXzzG9aHClv03BEpTKaMvJGRplAO4IqQAaS7DhisqMkkPshDSMZGXLl1q8Qua/NIDgx4U6RZtBSUqS8MHC40UMteQKlCK1BBIxCAsWB1cO7qi09qQbBOtEPmbpHK+uCNLI2JwRfigs2+ElCJzPviw+5H8VEDHqRC98847ratV2E1rmSAqS8MHIeT3I32KdcCwJyw3LI4ge2+KgzAQKOa9bISjaxniwXlJ8aqadEMUCI0I7l60t3vqqadsgbPACHRiZaTTRIaycKwWYiIE9OiDgYUR9WatqEXDh8WOcFAEh6vi9+VI5ZrikvBeUroIMTUtiBFijkCFFaO4ItGIgMWLF1s59JtvvmmuCbEGgpMEO1O1LgCzGiGiaAvBwKQm8MmdMWrKSzSA/SlYBP6oBYrisBrCpmQBiwIh4vfAVaTlAOXsTIvjfFSapvM3iwMSjSzDjk0CbNQEELOgmxYLmw9fOrBA2JRFWpW7IilVGueU192wPEUDWNCIMJYXxVvEObAa0ukjyt+LoChWzPz58y3NS8C60Os6woqGHLuQYGVwl6KUmapOWvmnE5lnPwqBTvaPsFAxw5kjwhCiQq8zIKvCde7Spcu61oUESwmapgquCpsDEfsVK1aUOXpBJEbZkxSg2Q0LOt1IPIJBcI47KdvjSRX26dMnrZhIpog6e1IWXG/cNmalMJu2a9euKTcXEhujYUkRQBfwdAUDrcbCIDZC9gVXJFcEI9fgehMMHjJkiLmHjKBkbgrBaBE9Eo1ywO+0ReUiqVpqMNgeL8EoHUQaV5CNejReRkAIaBLzENEi0SgHKDwaNGiQNZRhwxXNcyQYyaFGhdQzm9MIYPbt29fNnTvXe1ZEhUQjYmhCM3ToUIvgs62dVK0IT79+/ezaqdlw9Eg0IgafnC3hF1xwgQ1AUjAvNYhz0Now7B4VkT4SjYhBKMhMlGcNRlygNkaiGz0SjYjBnMYfp8WdEPmIREMIEQoVd4mEUAuBC8W+GpEbUM/DcO3isIuXJk8tW7b0HgmPirtERqB8m+pLkTvQSJot/jNmzDAXl/051PuMGDHCsnFR3f9laQiRJ8ycOXNdU+nBgwfbDmvK6wms04+WsRip9FuRpSFETKGFIRk3duoCrRToFEeD6XR3WYdBoiFERCxbtsz6g9BHljYILPgwUEnMOWgTwBhOv0UDvWjZERxVVze5J0JEAB3IKH9nJCUDs2rWrGlNlmivwIJPBnts2OU7ZswYi2Wwf4kBUZ06dXLdunVLqz1DTrsn6BPdtRmp5x+oZphNR5yD4A8Xnt4WmGz4dkLkMix2xjSwyY6GS+yZGTlypBs3bpz3irKhhQL9aAlQE8eg/wqNmoYNG2ZrIUoiEw0WO81r/G3gTZo0sUE5nTt3NuEIAudgO/kNN9xgvTiZC9qzZ0/r/ZhOYxYhsg0ZD25y/ueUzzJf01woCAgDrQDImgBl9HQ2o1iQ8RZREploYB3QeYkFj4lGh2i2htN2ja3OQeAcN954o6k2/0eEaI/H5iXa1QuRq9CrNJ2YA1Y5QVDcGh8CocQ4oiYy0cCcGj16tOvVq5cVo+CD0e6fYUJBG+di1jGWkIuFUgPKPW3aNFNtsR6sN0YfMEcWf1qUL4ygYHOdPzoBAaFnadCiLJoO8Zn3N+iRfqU1APEN1lOURCIatORncDH5ZSK9/kYtNhtRmEKbuyBw0TDRfMHw4TG5JxuCuGKNUfQT1JIT2YOeKT169LAdzqRH6QHLTmfGUCaDvitkS+ghS+CT4dmcjybLuPtRb3yMJHsyZcoUGy3IhaKlXarg0tDhatKkSetEAsVGrQcMGKCSZw9EeuzYsTbjg2vCFnJ6aiaDvxEfTkSGDusIfN26db1nRbpg8ZFmJRlATIKbJTNeksHnngbIvM+HsQvchOkYny45OWFt+vTpVrFGB2hatqUKLk2tWrXswnNw4fhwEwzF1dHO0bVgvREk5kPKNWPhl/XhJHtFGz2i+fydGP7EXFXcQSbFFXqL/0xBdzauJdeUgqyg3dqwTBAYRjj4B+fwg6LpknMjDFBH0qLklRmAkw4sgMaNG7vevXvbB5wpZP3793ft2rWznHWhwzXG18UKIzPFhwuSpbR5HiuDQUL8vUhhc2fD9J0zZ473KiHWknXRIN5A4BKrwLcE+JByNyOAGbajNA1mmzZtarMw8Adbt26d1gCdOMF1pfdomzZtTKC5QzGpLdk1xkNlcFDxehcew1JhNogQxcm6aBCkYVETNaZABfgg+t2kFcDMDAgDrgVpbLZPU/RDuTIWQzLRIC5EvKl4VSGPYQIHqVYUhUXWRYOADy4FO/AIzo0aNcoq4zCjGfmX7vwQsdYtIcYzfPhwK01GlGlgjIXHoKFkokEWi8g+BXf0Z0A8cG3YPcnfTojiRJI94YOLK0KdBiAkbdu2tQ94OgUvYi0ELCdPnmzbpamH8d1ASpQnTpxo15lRCckYP3689Wsge8JOSkTD31Ep4kvY7Ik2rOU5BC5nzZplRVzEMUiGEVWnPoNAMfUa5PQ5KAQSoiTqp1FgECcijkEgk41MlBsTJyJehAtIcJR9C1FvahLxRZaGEAWOLA0hRFap8Nufq2VpCCEC4tz/AYC0sPORJ+sTAAAAAElFTkSuQmCC)
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAATCAYAAABC8OWoAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAA49JREFUeNrtWl+EVFEYv8bKyFiSJCuRlZU1hqyVlTUvKytjLfswD0mGkaykl5XsQxKrh2RlGclK0stKshLJWmtkGdmHZC09JMla5mGskXGZvk+/m9vZ79x77u69M3Tvx48735xz7jnf+Z3vz5mxrETiLm2gRagS+hOTJGIiKcJ1wqcgnbjDXGK7WMsv1/McOCFKlvAxsVesZZSwquiq4MYe4S9yEcbJOMoZwixhw6NNL2GBsA5UoOu0nAAHTiv6c4Q1tXEOjb2knhAmsDwnlH3W/4FQcH2+BF2nib0M0kiyBuL8lQeE6Qg3Pa6E8Vv/FGFe0D8iFDvoWd76eLUbam77jnDBoPRqaxZfgDvl0myLMOJhsGHCG8IhYRw20nckXouEtGYcNvRXtOOYe9LQOIdxOHbQd4nwmDDTJcLw+8cEfR7fqf3HCTXX3DOu9uvQV+ExHOEQs0JoavaPyTLgM//zqtdraDbQ1Eu8IJzF81XCZ01fZ/JHhDGYSJvY/BRc+UNhnCls+inX+1YNNq0H7WbwzLhFsAkThgelbXB4gtiurrE767aV/mXYzrHzFXincUV/GaRypKaEPJM1SvNpuBV2iGElBU+j9j2GU6CLk68EN/xTGCdv8D5JOPm8L+i3POYUtYfxsntL6b+EtaolcEXQu8dtag5oUGlFRRipbRsubdijzy7huKJrGM7BZG5MvqMC2Xa7mMPYhvchbSE8++kdmUCYKoZJmIOGpFmcVFvj1vjzEHKXTED3HwZhxNIQBF4J6K7DDEnbGrunhZAUZFxVzzZ/Qvii5DemsickvRcSVdPJVZBXpH08jLNBy5pTUUdSup85+G3cJEpcKcle7KKH4TBzUdCPaZLeg9rjthXw6l+X9JqU1S0hVkphw/LxDPzy1wJpeONKERGGk76XmnuSUhcJM4mTbwm2KEZAGNN8T5VpcCTQxd2GJg5uuozeR7iHfKHPYwEjSHLdpOlHqeyUmVwFPQuJML1w8TnXevkE/7D+XId3izAWQuJNVG3s+u8IVV9YhCn5hGDL9OKOhX9Hynp0ysPo6mSycHMtVEEcdu4axOBRkKbHpRsCcW2U5oUQk14e6xvmWQMxdzReM0yi+OU8XME8RZLbRIjPhEgY57027lyCVoS6/C92Pz4OasJUIv9K1cuRXLP+z7838E3mgut0OZ5sIOGDp3DeUo7jwtnFz+POpQnXPJjwIbj8Bi7uIm3cD159AAAAz3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtZmVuY2VkIHNlcGFyYXRvcnM9InwiPjxtcm93PjxtdGV4dD4mI3hBMDt0YWtlbiYjeEEwOzwvbXRleHQ+PG1pPmc8L21pPjxtbz49PC9tbz48bW4+MTA8L21uPjxtc3VwPjxtaT5tczwvbWk+PG1uPjI8L21uPjwvbXN1cD48L21yb3c+PC9tZmVuY2VkPjwvbWF0aD5ML1ISAAAAAElFTkSuQmCC)
A block rests on a rough inclined plane making an angle
of with the horizontal. The coefficient of static friction between the block and the plane is 0.8. If the frictional force on the block is 10 N, the mass of the block (in kg) is : ![open parentheses text taken end text g equals 10 ms squared close parentheses](data:image/png;base64,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)
In
then the triangle is.
In
then the triangle is.
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
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)
Two masses
tied to a string are hanging over a light friction less pulley. What is the acceleration of the masses when they are free to move ? (g=9.8
)
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)
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
A machine gun fires a bullet of mass 40 g with a velocity 1200 . The man holding it, can exert maximum force of 144 N on the gun. How many bullets can he fire per second at the most?
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
One end of massless rope, which passes over a massless and frictionless pulley P is tied to a hook C while the other end is free. Maximum tension that the rope can bear is 840 N. With what value of maximum safe acceleration (in ) can a man of 60 kg climb on the rope
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
Three identical blocks of masses m = 2 kg are drawn by a force F with an acceleration of 0.6 ms–2 on a frictionless surface, then what is the tension (in N) in the string between the blocks B and C
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-
When forces are acting on a particle of mass m such that and are mutually perpendicular, then the particle remains stationary. If the force is now removed then the acceleration of the particle is-
In above problem, the value(s) of F for which M and m are stationary with respect to![straight M subscript 0](data:image/png;base64,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)
In above problem, the value(s) of F for which M and m are stationary with respect to![straight M subscript 0](data:image/png;base64,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)
Consider a special situation in which both the faces of the block are smooth, as shown in adjoining figure. Mark out the correct statement(s)
Consider a special situation in which both the faces of the block are smooth, as shown in adjoining figure. Mark out the correct statement(s)
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction
In above problem, choose the correct value(s) of F which the blocks M and m remain stationary with respect to M0
Imagine a situation in which the horizontal surface of block is smooth and its vertical surface is rough with a coefficient of friction
In above problem, choose the correct value(s) of F which the blocks M and m remain stationary with respect to M0