Question
If reaction is R and coefficient of friction is
, what is work done against friction in moving a body by distance d?
![](data:image/png;base64,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)
The correct answer is: ![mu R d](data:image/png;base64,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)
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/generalfeedback/903707/1/903671/Picture5.png)
As shown a block of mass
is lying over rough horizontal surface. Let
be the coeeficient of kinetic friction between the two surfaces in contact. The force Of friction between the block and horizontal surface is given by
(![because R equals M g right parenthesis](data:image/png;base64,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)
To move the block without acceleration, the force (P)required will be just equal to the force of friction , ie ,
![P equals F equals mu R](data:image/png;base64,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)
If d is the distance moved , then work done is given by
![W equals P cross times d equals mu R d](data:image/png;base64,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)
Related Questions to study
The force
acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory
![](data:image/png;base64,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)
The force
acting on a particle moving in a straight line is shown in figure. What is the work done by the force on the particle in the 1st meter of the trajectory
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAM0AAADSCAYAAADpPEQnAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAABrQSURBVHhe7Z0JcBRFF8dbIMidgHJfViCABSgRELE4/EDlKOUyXKJcIkgZDuUoDrUKueUWFEQOYzhUlBu5w+mBIMEClEMEhIpaiECCoqLut/+2O06W3c1Odo6emfermpqZ3s3uZnf+069fv37vNp8fRhBExOQTe4IgIoREQxA6IdEQhE5INAShExINQejENaI5cuSIOCIIc3GFaNauXcsSExNJOIQluGKeJj4+np09e5a1bNmS7dixQ7QShDk4vqdBL3Pu3Dl+vHPnTuptCNNxfE9TtWpVFhsby44ePcrKlCnDateuzdLS0sSjBGE8ju5pUlNTWf78+dmIESP4+YoVK9gnn3zCTpw4wc8JwgwcLZrx48fzXiUmJoafV6tWjU2fPp2lpKTwc4IwA0ebZ1evXmVxcXHsvffeY927d+fOgLvuuiu7nSDMwNE9TShhkGAIM3HFPA1BWAmJhiB0QqIhCJ2QaAhCJyQagtAJiYYgdEKiIQidkGgIQickGoLQCYmGIHRCoiEInZBoCEInJBqC0AmJhiB0QqIhCJ24IhtN4CI0uzh16hQbNWqUOLsVrCxt2rQpa9eunWghnAj1NAZSoUIFNnbsWFaqVCm2Zs0a1qBBA36OrXfv3uzMmTOsffv2XDjXr18Xf0U4DeVE88MPP7DbbrstxzZp0iTxqNoUK1aM1a9fnycuBK1ateLn2NC7rF69mg0fPpzt37+fjRs3jj+HcB7KiWbmzJni6D+SkpLEkfPp1q0b3yMBCOFMlBINepl169YxDLO0W40aNcQz3ENCQoI4IpyGUqJBL3P69GnWr18/tn79etHqHnBTGDp0KD9+5ZVX+J5wIP47uRJkZGTAi5dj69ixoy8rK0s8IzQrV67kzz979qxosZd58+bxz9OkSRP+P2DDsfy/du3aJZ5JOBFlepry5ctzU+zQoUPMf9HxNnigevbsyY+dyIABA7K9Z0hsCCcA6N+/vyt7Us/wr3bUAz2MvDvndmdWtafx3wBEy3+cPHkyu8cJ9jihPsp5zyRw337wwQf8+Pjx43zvBuDU8Jtr/Pjzzz/ne8JZKCsaAJNNXmBu4tKlS+KIcCJKi0ZSuXJlceRsEAXwxhtv8MlN0KlTJ74nnIXSosFFhruyU2K1EHsGISQnJ/NzhNHgXG7Fixfnj6H39I9teE9KOA9lAjZxB0ZFsxdffJFfTDL4ccqUKblObqoSsAmRQwzhqFmzJh+vEQ6GuwMUYN26ddlepYSEBN/w4cMjmqMBqnnPCHdDSwMIQieOcAQQhEqQaAhCJyQagtAJjWlMpmvXruzChQusYMGCosV9oAw9vJ9egURjIosWLWLPPvssu/POO13tZsZcWqNGjdjOnTtFi8uBaJyOqi5n/4XEP5fblwIkJSX5/D2p78aNG6LF3dCYxiR+//13lp6ezvLly8cKFSokWt3JyJEj2Z9//sl2794tWtyNkqJJTU11/A+wbds2fiGtWrWKPfDAA6LVnTRs2JAVLlyYLVy4ULS4G+VEgzv0oEGDWN++fUWLM5k2bRq/kLwSlIkxTVpamjhzN8qJ5qWXXmKZmZl8Pf3atWtFq7OA8A8cOMBatGghWtxPnz592LVr19iRI0dEi3tRSjQ//vgjmzNnDs919s8///DgTSeyadMmdvPmTTZ48GDR4n6wLB3jt3feeUe0uBelRIMMLWXKlOEh9G3btmUXL150ZG8ze/Zsbpo1a9aMlSxZ0hN3X1CrVi3HWgd6UEY06GWQSAO+fvQ0sbGxfMJs9OjR4hnOQGua4X+6evUq37zAE088wc6fP8//bzejjGjgLZs7dy6/W0kwMQjPjJN+BC+aZhKY07jhrVy5UrS4FDFfoxRxcXG+Xr16ibPcUWlyExl0ihUrJs58vg4dOnhqnU/FihV9devWFWfuRDnvmZOBafbpp5/mWJ4Nk9NLa3xat27Nvv76a/5duBUSjYHAcwSvH+aZvArM0r///ptt2LBBtLgPEo2BLF68mHv+3B4BEI577rmHB6cuWbJEtLgPEo1BwBw5fPgwe/zxx0XLv2zZssXVpkowmjdvzvbu3SvO3AeJxiCCmWbw+rVp08ZzmTSfeeYZ9ttvv7n2/ybRGEQw08xrPYwEed2w6M6t0QEkGgMIZZq5fUlAODC2+eijj8SZuyDRGEAor1m5cuXYZ5995knHQI8ePdjPP//ME0C6DRKNASxYsICH/QQTB9q82OM899xzPDoAa6PcBokmSmCaHT161FXFdI0ANwpM6i5btky0uAcSTZS8/fbb3DSTVc6I/4BD4Ntvv3VdwCqJJkpgmt1xxx05Ak0l6IXgcj5x4oRo8RaIDsANxW3RASSaKMAdFILo0KGDaMkJ5mkwuen2UPlQVK1alZUqVcp1rmcSTRQgrxmZZuHBuiIUsXLTnBWJJgowngllmgG4nBH1i71Xkemd3BQdQKLJIzDNTp8+zbp16yZabgUepM2bN4cUlRfAIkJ8D25KW0uiySPz58/HAr7sUoFEaOrXr8+2b98uzpwPiSaPIPQdOZq93ItESv/+/Xl6J7d4EUk0eQCm2ZkzZ3hFgNyALe/VwE1Jly5deHqnpUuXihZnQ6LJA9I0y81rBldz48aNPbc0IBCMaVCg98MPPxQtzoZEkwdgmlWqVCnXtf9e72G0IMzou+++c8WcFYlGJ9I0g8mRG14M1AyFTO+0evVq0eJclBRNhQoVWHx8vDhTixkzZnDTLJLkGZifgcvZyzkDJHFxcaxs2bJ8sZ7ToUpoOkFoCEAmSUIfvXr1YsuXL2fXr193dC9M5pkOYI9///33YSc0idCMGTOGp3dC7R4nQ6LRwaxZs/h+4MCBfE/oAx60okWLOr74E4lGBzADq1SpErEJ6PWlAcFo0qSJ49M7kWgiJC+mGf7Gy0sDgjFgwACWlZXl6PIjJJoIIdPMGLCaMyYmhi/ecyokmghZsWIFq169ui7vHFzOcLViI/6jdu3abN26deLMeZBoIgDmFaqyoV6OHuBWvXLlCqtXr55oIQBKDeI7dWp6J1vnaeCvP3nypDgLD8LLQ2H2PA1ms2GeoXiulxeUGQUcJEWKFGHjx49nY8eOFa3OwVbRnDp1iuf9xXJYAM9K6dKl+TE4duwYX+iF52BpcSjMFk3FihV5JvxIBU7kDryQJUqU4L+x44Bo7CYhIYFXMguGXzA+v/0rzoJjZiU0f+/CX3vq1KmiRR/p6eniiNCSnJzsy5cvn+/GjRuixTnYPqaBiSZ7k2CgqhiSM9jFhAkT+B52uF4Q3JmYmMjriRI5wbIKJCVxYr5n20WTlpbG99qSewDjB4B2mEZ2gTUgNWrUyNNYBqIhgoMYPiQlQXISp2G7aNavX8/32t4ESRgyMjLEmX1gDPPTTz+F7AWJ6MAYFgniHYcw02whKyuLjxdQEfnQoUN8mzdvXsjxTSjMGtP06dOHvy7GNXll8uTJUf29m9m7dy//fnft2iVanIGtosEAX4qmY8eOfMM5Bv96MEs0pUuX9tWqVUucEWZQqFAh35NPPinOnIGt5pk0zfbt28dX9GHz33XYQw89xNvtBKbZpUuXPF2p2QruvfdetnXrVnHmDGwTDbxmWMUXOF7Aqs37779fnNnH1KlTeQYV/11QtBBmgFi+y5cvOyo6wDbRhPKawVOFzW42btzIY6SijRsbPXo0RTmHAWmw8ufP76g1NraJRmaSt3MOJhTSNEM1r2jA3XPKlCm0niYMiM/DTfL9998XLepjuWgQOgOX8po1a1hCQgI7dOgQN9VUgkwza4G1gfROTpnXslw0r732Gtu5cydfV1GnTh32+uuvKzEnowUOirp160ZtmuHvcSd1chIJKxg1ahTfp6Sk8L3yCC+aozHS5XzkyBH+Wn4bW7QQVlCuXDlfo0aNxJna2DamURWEq2Ng2rlzZ9FCWMEjjzzCDh8+7IispCSaAFASAmYjrba0lmHDhrGbN286IukGiUbDV199xTIzM/kPSFgLJjmR3gnJ5VWHRKPBaNMM3qDChQt7vmpApCCAE04i1SHRaIBp5h+MGubtgmhgo1P1gMhA8Sekd1J9XotEIzh48CA3zaKd0CTyTqdOnViBAgXY9OnTRYuakGgEEydONNxrhnwFkydPphKDOoATRvUAThKNYMeOHdymNnoiEhN3lMEmcpDBFOmyVI7XI9H4gWn266+/0gpNBUDaWhR/WrZsmWhRDxKNHzNMMyJvYH4M+QPeffdd0aIeJBo/ZplmAFHOtDRAH4hLPH78uLJeR8+LBoIxyzTD0gCsp6GlAfqAiYb0Tps2bRItauF50cC9efvtt5NpphAo/lSyZEk2d+5c0aIWnhfNnj172P/+9z9TTDNaGpB3mjVrxr744gtxphaeFg26f9jNQ4YMES3GAtEg6SFVd9ZPcnIyu3HjhpIBnJ4WDbp/mGZmZr+haOm88fDDD7OCBQuyJUuWiBZ18LRozDTNiOhp0KAB+/jjj8WZOnhWNGabZkT0IIATCU5US+/kWdFYYZrR0oDoQHonRAfIzEWqEFQ0yBYjwxgwkMUHnzRpEj+3gxEjRhhersIK04yWBkQHfhu4n5cvXy5a1CCHaJBKqWnTpuzatWusQ4cOotUYIESIT25I5RQMhIdrn4cNtS5ffvllw4SL9FFkmjmDpKQk9dI7iQQbHCQgT01NFWfGk5GRkV0VANvJkyfFIzlBNQFUR9M+jjYkSg/2+fRmo/GbZDzxthVVuPw3H1MqtHkFVFzAbzt//nzRYj/ZosHFDNFYgRQNhAExBCPYZ4GIgolNr2hiYmIs+1+J6EH1BtwwVYGbZzDLMJnUu3dvnFoCysehbGCbNm0izrCJ9KWIEUPCwbyCorbIejJ48GDRQqhO69at2YEDB8SZAkA5MHlwGOyujxoyuCujJwJ4DtqgfLThro/H8feBJlUoxNtm/51fQPxcS6ieQNa0gakn0dPTICFd0aJFxRnhBGQCx61bt4oWe+FXL4oo4YIPBBco2vGBpWi0YxLtGEOaTnit3MDzgByn4HzixIm8TRJKNKiWhufjs0n0iMZq02zWrFm+K1euiDMirxQpUsTXqVMncWYv/OrFBZfbRSpFA2Rb4IUOAURie+JvJegxcI5NK4RwF3bge0cqGvk8q8rVyUGs08rjqcijjz7qi42NFWf2EtXkpv+fEEf/4h+wsf3794uzyChfvjwvbQHat28f8XwMqg3oZcaMGbxStFWV1mh+xjiwxgZTISqsTVIiIgADfH8vw48x4RhqDida/LYxe+yxx8SZ+VBMm3G0bduWp3dClQm7UUI0ADVK/OMjfoxZYMQchQPBfHrAmvO//vqL37GsAlloUPKblgZED25ASIW1efNm0WIfXDRw4x47dow32MlTTz3FXdEglJkneyHkx9IDYs2sNM0kEAz1OMbQp08fHrxpd3QAFw3u8pgzCTZf8s033/A95jcksi09PZ3vAf4W4SkgnHkl3wMxbcGYNm0aT6wQCmnTNmzYkO8jxWrTjDCevn378rCqRYsWiRabgDcArl8car1XQOtelltgG7xc0pum3dAWCJ4b+LxgSFd0MDCnE+jWzs17lpKSwh/3m0qihXAqlSpV8iUmJooze8i+aiGGYHM1dqGdvJRI97TeMBr/+McXFxcnzqwDsW1+88zn75lFCxEtzz//vK9AgQKWxA2GItsR4P8wfJyAMHwVgCtaC8y6Ll26cGeBnpLpcPuiwlb37t1Fi3Ug3xnW0lDeM+MYNGgQd+jYmd4ph/cMHqYzZ85w4UQaD2YFGP8gRg0bnAV6WLBgAc+h1bNnT9FCOBl4VjE/iKUmdpFDNPAurV69mme7X7t2rWi1n5kzZ/KCS2PGjBEtkYPEDMihZYfbFy5nBBvqTYCOC0JPb+o14AG1Nb2TMNMcTagxDezefPny+QYOHChanAH+F2wUfhOc7du38+/nwIEDosVacvQ0bsOJptn69etZQkICP1Y5c76dyPROb775pmixFleLxk7TLK9gchf5CyCcxYsXh5zP8jr16tVj27ZtE2fW4lrRwGuGzPMoEmQn8J5FGrj55Zdf8nSs8BzK/AUYYxK3gigW3FDs8Ey6VjQqmGb4QRs3bhxxCieUA/ePv/gxEoyAOXPm8D2RE/yu/vEqW7hwoWixDleLBl4rO00zPUsDcNfEEon69evzc/Q2uJsivMno9FVuAPF88fHx2UG+VuJK0eBixcXWo0cP0WIPegI14VYPnFiWc1LkEAgOemOkd9JzczIE4UVzNIEu5/Hjx/NzFcJXEO+WW8iHjP0LtwULK/I6+L3x3SxdulS0WIMre5qUlBRumqlQijySpQH4vPPmzcMN7JYN7YAcAreCSfiyZctaPq5xnWjQVSMUyG7TLFIQroRlF7169RItOdE6BFQKbVIFzNkgttBKXCcapK7FHbpfv36iRV0ggnHjxomz4BQvXpwX0cUYDc8l4eQE+ev++OMPa4s/+S8wx6Md01SvXt3nN83EI/aCsUzr1q1Djq3wmbVbsDVIgc8J9Twvg/ROXbt2FWfm46qeJjMzk5tmoUwdq8E8zZYtW0JOwPm//xybdDdrCXxOqOd5mUaNGvHv2SpcJRrMzeCisjK9LmE/qCqB9E5WFX9ylWg2btzIqlSpooTXDMjJVb1LAwh9IKcEogNQ3t4KXCWaixcv8owlqgBXM1I4qSJit4LvuW7dumzDhg2iJXqQiCVU1htXiYZMM++CUoMXLlwwLL0TRAMhBuu9XCWaqlWr8gkvwnsg0BU3TaNi0XDzXbVqFXv11Vf5BKp2JfNt/jeCG9PRYN0MghsrVarEqlWrJloJr4EaNkhda6R3EZPlmDyNiYnhN2TU/3SFaM6fP88nAAG+NMKbXL58mU/+wuIwCsgDEejIgIOJZkyeKy0afAGoDoDFZKBy5cqsRYsWPAEIQQSC8QycAnqiy8OB+bXmzZvzjLFwa6MCX1xcnLpjGmRkgbK1WeKRshZtdqbvIdQFF7RRgkGuBqSLSkxMZGfPnuVBoXh9Dnoa1UDaWXy0YNlYkDoXjwUrOUgQRrFmzZqQGVuVEw0qnEEUSJMbCggmt+cQhFkoNabBGAbmF8jKygo5dsHArEKFCvw43PMIwgyUGtOkpaXxPTxh4YSgzfMsSw+qBoSNZcpYoiDXxBDuQCnRYEYXoHZnbsgaNpFmerEarPl/6623eO4yO4HnB6JFXRdsEDEEbTawGpDzQL4vPoNZZSFzA4N6fAajcFVEgErA07dv3z5xZg8QBzxAstgWgIhh2potHCyYQ845WP+YNsBnsKOoFsSLAshGopRoMA8DIillKC8EJ2XPtBr0dsgxgHGfvHjlJLCZOQeQ9BDzGnJmHnsUIsbqUzxmJUOHDhVHxqGUaDBxCfDlhrsTah+jBVmhQUpe1B2S40N8V7Nnz+bHZoL3Cax6UKJECb638veSAg1XjjIvKCUa/LgTJ07kx+HuhPIxmamFCE640iS1a9cWR9YAp4iVThuYZehlzLhJKDemQaIEmBDJycl8ABcI2vAYEoXjLkroA0WG8f1aVeUad3s4AdDryWkCK0BaLJS/N2U6AvM0qoHkeXKSE8VtMYmJzf9jO25SU/4PKoDvFXVVrUrMgd8J/7/c8N74DGaDmqza7xzHeH+jUFI0EnzBCJuRokFYjRVfupGoJBrciFJTU8WZNcjfEILBd4HPYDb4vrUZST0lGjegimhw4doZrycrc5v9XeCmEHhjMFo0NE/jATCpCDc+5o7sAlEc/ouXlSpVSrSYA5xETz/9dPakKjY5PSHPo4VEYyLw4IBLly7xvR1AMKNGjeIOFomcrbd6hh7C1VudWy8Qjb8zyLFBrECeRwuJxiTgMZLBp/v37+d3OKvXAUEUMiIAn0XeaXGMyUazKkjz1Y3+95HeTylSzMxb5bUzFb/yCBcCDxJ+3lCbmeMbOGy074UxBcZUdmH0mMYVOQIIwkrIPCMInZBoCEInJBqC0AmJhiB0QqIhCJ2QaAglQAj/hAkTrC9vngdINDaBCT/tjDzWm1g9Qx+I1asqtSDh+O7du/nqXRTuVRkSjQ3g4rjvvvtYRkYGP8fFingphLvYydatW1nTpk0tSbwRCLJX7tixg3Xu3Jl1796dxcfHW1oSUBd8ipOwDMyMY12QNnQdIDIXs/h2g8+HyyLw80lQfDcmJiZ7tt/MrWDBgr6xY8eKd1YHigiwEJhfyMiyZ8+eHLnbVAMxcjCRQmXTQdoss8YeKKY0cuRIHruGgsOoD6Nc+UUuHcISEANlxSIsI8CiMatXyA4bNoz3MG3btg2ZR1kFaExjEBjYB+Y0wDnu2ngM4xZEGyclJYlHc4LHtQNx+XpyfCFfK5LBOv4GjgWA18ExNhzLttxeDwPzOXPmiDPzeeGFF3hJlfT0dLZp0ya1K9oJ8RBRoF0Lj2Ms8UWPIpdpy/NgXzfW68ulwPLOrn09jHXka8kcCeHW+MuKC9gwRsLfyvfG36MNEc65vR7acnsvr0KiMQAMnrUXphSKFrTDPAsEA24pEuwBQutlOLs2hF+G+8vnBQMikyLUXvDy82EvkUuQg71euMe8DplnBtCuXTueY8x/gfEFZ8gpFpg6CO3BgEMgMEsoFmq1bNmSHyO1q0QuGoMJEwqsjKxTpw4/1ibmi42N5ftWrVrxPZDOiGCvF+4xr0OiMRBZHSAzM5PvzeKXX34RR8YQ7vWMfi83QKIxkIMHD/K93YnPjcTsRBhOhERjICgV4h8zsOnTp4uW//CPacSRM5CeNtScJHJCookS6WaGSxfm2YMPPsjPMZGJTbp027Rpk51KKBTnzp0TR8GRF3I0ZGVliaPwr3dS5F2mqgxBEA4BIo/gK4SnSxbVhdcMbXD9aj1V0vOFvRZ4uKTrFxu8VTKUBRsew3Owad3J2tfWIr1k2PB8eMHwetKjhtfDeW6vh8+BvyFuhcJoogQ9zN13353DU4WATDgD4FXTgp6oWrVqOZL2oScKrOaGSF9ZFQ7Iu33g84IlgA9ME4X3xFhL+3p4/YoVK4Z9PXjqhgwZQknmg0CisRCYazVr1uSmj1k5x4wANwKUPnSTQ8NISDQWgzEQkuapKhz5+fxmndJBpXZCjgCLgcnmH0/waGeYcSoB0w6mIwkmPNTT2AQ8V7g4VeptML6ysryfUyHREIQuGPs/p3oBU/qO/igAAAAASUVORK5CYII=)
The pointer reading
load graph for a spring balance is as given in the figure. The spring constant is
![](data:image/png;base64,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)
The pointer reading
load graph for a spring balance is as given in the figure. The spring constant is
![](data:image/png;base64,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)
The force acting on a body moving along
-axis varies with the position of the particle as shown in the fig
![](data:image/png;base64,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)
The body is in stable equilibrium at
The force acting on a body moving along
-axis varies with the position of the particle as shown in the fig
![](data:image/png;base64,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)
The body is in stable equilibrium at
A frictionless track
ends in a circular loop of radius
. A body slides down the track from point
which is it
height
. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
A frictionless track
ends in a circular loop of radius
. A body slides down the track from point
which is it
height
. Maximum value of
for the body to successfully complete the loop is
![](data:image/png;base64,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)
Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is
![](data:image/png;base64,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)
Velocity-time graph of a particle of mass 2 kg moving in a straight line is as shown in figure. Work done by all forces on the particle is
![](data:image/png;base64,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)
Domain of definition of the function
, is
Domain of definition of the function
, is
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
If
represent the work done in moving a particle from A to B along three different paths 1, 2 and 3 respectively(as shown)in the gravitational field of a point mass m. Find the correct relation between ![w subscript 1 end subscript comma w subscript 2 end subscript a n d blank w subscript 3 end subscript](data:image/png;base64,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)
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)
Given below is a graph between a variable force
(along
-axis) and the displacement
(along
-axis) of a particle in one dimension. The work done by the force in the displacement interval between
and
is
![](data:image/png;base64,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)
Given below is a graph between a variable force
(along
-axis) and the displacement
(along
-axis) of a particle in one dimension. The work done by the force in the displacement interval between
and
is
![](data:image/png;base64,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)
A particle of mass
moving with a velocity
makes an elastic one dimensional collision with a stationary particle of mass
establishing a contact with it for extremely small time
. Their force of contact increases from zero to
linearly in time
, remains constant for a further time
and decreases linearly from
to zero in further time
as shown. The magnitude possessed by
is
![](data:image/png;base64,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)
A particle of mass
moving with a velocity
makes an elastic one dimensional collision with a stationary particle of mass
establishing a contact with it for extremely small time
. Their force of contact increases from zero to
linearly in time
, remains constant for a further time
and decreases linearly from
to zero in further time
as shown. The magnitude possessed by
is
![](data:image/png;base64,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)
Let
be a set containing 10 distinct elements, then the total number of distinct functions from
to
is-
The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.
Let
be a set containing 10 distinct elements, then the total number of distinct functions from
to
is-
The domain is defined as the set which is to input in a function. We say that input values satisfy a function. The range is defined as the actual output supposed to be obtained by entering the domain of the function.
Co-domain is defined as the values that are present in the right set that is set Y, possible values expected to come out after entering domain values.