Motion of Two Bodies Connected by a String over a pulley on different planes.
Consider a light inextensible string passing over a smooth pulley, as shown in Fig. 1.25, so that the tension (T) in both the strings is same.
Consider a light inextensible string passing over a smooth pulley, as shown in Fig. 1.25, so that the tension (T) in both the strings is same.
Let mass m1 is greater than mass m2. Since the string is inextensible, the upward acceleration of mass m2 will be equal to the downward acceleration of mass m1. This acceleration is given by
![Acceleration of bodies hanging freely over pulley Acceleration of bodies hanging freely over pulley](data:image/png;base64,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)
and tension in the string,
![Tension in string of bodies hanging freely over pulley Tension in string of bodies hanging freely over pulley](data:image/png;base64,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)
Let us now consider the following cases of motion of two bodies connected by a string.
1. First of all, let us consider the motion of two bodies connected by an inextensible string, one of which is hanging freely and the other is lying on a smooth horizontal plane as shown in Fig. 1.26.
and tension in the string,
Let us now consider the following cases of motion of two bodies connected by a string.
1. First of all, let us consider the motion of two bodies connected by an inextensible string, one of which is hanging freely and the other is lying on a smooth horizontal plane as shown in Fig. 1.26.
Since the string is inextensible, the tension (T) in both the strings will be equal . The acceleration of the system is given by
![](data:image/png;base64,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)
and
![](data:image/png;base64,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)
2. If instead of smooth plane, it is a rough horizontal plane, as shown in Fig, 1.27, then frictional force equal to:
and
2. If instead of smooth plane, it is a rough horizontal plane, as shown in Fig, 1.27, then frictional force equal to:
will act in the opposite direction to the motion of mass m2, where u is the coefficient of friction. In such a case,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAADKCAIAAACT57MIAAAgAElEQVR4nO1deXwUVfIvThHwByqIgFxBXEVAgd1VDkEkknBDAOXQNYlcK6eACoIniIJyg+EQogI5EMIlKKegqLiu6PpBXSDgxRXCbQISyNTvj69dW9NzZKZnJpPB/v6RT6en+73X/b5dr169qnrENmwEBgp3A2xEPGwO2QgUNofCjHXr1jHzlStXHA5HuNtiETaHwozffvuNmfPz820O2bAIh8Nx5cqVK1euXL58OdxtsQibQ2FGvoFwN8Q6IoZDkPYQ+AcOHJg7d+7ChQvfeuuthQsXTps2DReEu41WIA8VuYgkDoElL774Irng/vvvD3cD/7yIPA69+uqrRLRjxw75qW7dukQR8yBXHyLm1UP3ZOa77rrLxJjp06fbHAojIubVi9KAwYuZQSlmbtu2rc2hMCLyXr1J+zl9+jQRjRw5MoxN+pMjIjnkCo7YedlVgIjk0J133jlo0KCEhIRBgwY1adIEHIr0GXLkImI4JCtKRPTZZ5/J+alTpxLR9u3bWdl8HQ4HxFJ+fn7k2n8jBRHDIXDipZdeEqkDSk2cOFHGMtGywZuvvvqKbfkUekQMh0CF119/XUsdZn7hhReqVavGxjTt+eeflzmaafpmI0SIMA6JBi244447ME0TShFRTk7Os88+a+vahYOI4RCGJyKqWLEiMzscDpwZNGiQ5sqMGTOIqEWLFmzIoQA5BNUqLy/P7Xlb3+II4hCoIB2Wl5cnPjda4wFviOjjjz/GcYB9fOXKlYh27ikERAyH0ItQbiCEdL+ip9ngUMWKFYmodu3agdcrYmzPnj3z5s17y8DSpUtbt2797rvvTp06NfBaIhoRwyGZq2tvm6+//pqNCbzmEA5efvllDngsk+r++c9/ujVv2sssEfP8WuqY5vmaVdCEmJmINm7cyC5ze+gxgfgv//TTT0S0a9cua7ez0qW88Fu+GRi9pLUHDhwQcbjYwJtvvpmZmWm6kQtrThoxHNLAC8I8n51fNzt7dbn2E4SWeAFYwLhx44ho//79bNWDDCqa9wZcunTJRPTDhw/HxsZ6koVAdnY2WgV9sXDmpBHJIT3Pnz59OhtWbPlq5St0qw7jYgscQrGTJ0/Wdk4LHMJEz8cbDxw4sGTJku7du3tnj+Dtt99m44uyOeQNP//8s1ZHZHQAM6AeoYNNXNm8eTNbNV7jrgceeEDkH754f8uRroXG5hYHDhxISUnR5ChWrBgRxcfH68YIKlWqJFdqg1khICQcQndKv0pHiiIS+PeBJQ7hkEluuw5qOEhPT1+8eDFbfb+itteqVYv9HMikhWJrELcnzfLMzMxly5aZqFOsWLHixYv7orxXr14ddx09epQLy74aEg55erOizwao6x0+fJiIihcvXqJECSLC7NrL+0JnywXavd8vyBhqYT4P6uBvdna2/gCYef78+V26dNHUGThw4Nq1a1n5umzatAklOBQwXovmtGvXLlzcrFkzLixRFKqxbNq0aaZxuk2bNmw8VYDfx7333osPFF+nLtkt8N4vX74skVxi5vYLIodeeOEFf+8V1sJpjoiOHz9ORPgMgCFDhvTu3Xv16tVyV0xMDH7CEOxdTUb5I0aM0KKoEBAqDuExhg4d+tBDD23YsAHfB4J4Ao8L1voB8Nprr3m5Hl+qiB/510LVr732GhG9+OKL1lqO8QvYtWtX586diah27dq9e/d2vRhGBCJ66qmn2JDi+Ak6GRATE4NJonwVOH/vvfdaa6S/8IlDIjOhPxY4Nd2/fz8R1axZ06kmQ3RbmxMJ88aPH08u+Otf/+rLU5gOLKB58+bk4norJhx0sx5u5Bo9fpk+AFNRcteECRNwAfwUQKD9+/d36NDB9Pj333//4cOH5dGeeeYZnP/pp58sP6nv8E8OmRQLT9i5cycRTZkyhZVbDxHdfPPNbDW2XGiXkZERFxe3YcOGQ4cOEdHevXs//PDDli1b+lugNdx+++3kotvK4Og61iQlJUHYeIHufo0WLVq4kgwkBsaMGYO4KEDMjB999BHOWBhzLcBXDjVs2HDv3r1sfA1Tp07ds2ePp4th/cPIBZw9e5YM2641fVY+dDnz5ZdfmmopBHTr1q1EiRJu2ybs2bdv3/z58zMyMjRRHn/8cSg6eIQ1a9b07ds3ISEhPj4+JiaG3XHolltu0cKbmdu1a4czt9xyi1y2efNmnHzmmWfY6KDbbruNiBo1ahSa1+AEXzkkTZS5ydNPP+3p4kmTJrnKbZk9WRvLZJhgpZIT0fPPP4/jouCDkZmZmZ6eLg9eq1athx9+mH1Yc3Ar3Vu1aqXlEJRxvEx4A+v3QEQTJkxgo4Pq16/vKsNCBD84pAWjdzkZFRXlVmizseQunjeuwl+bm/X0VU9o9buTZmhzlKcyLejRuhm6DXJBZmZmcnKynplHRUXFx8dnZGSYinK4eKq4/qoxatQoIrr77ruZ+ciRIyhcG4q0nkDOmn5SUlJR5NBLL72k//UyN8EDsBq2RI0AIUwTJX2vw9kyKX1v6j95d5MnT/b9aa2NodJaTcEZM2akpaVp6tSsWRNSJ1jAojKkS7NmzfTX+OCDD7KLHBo/fjw7LwS9/vrrQWyPJ/jBoVdffVX/64VDrl8A1EMci2C3bCX65ptvpKJu3bqlp6cvWbJk8eLFycnJixcvXr16NRFlZGQsWbJkyZIlKSkp6Om2bdtaq06PRKbpFRENHTq0d+/eWupYNhyYgOwUcXFxaWlpqKt+/fp33HEHjtu1a8fK2kTKhsTKMhl4MwqEr3VERUXpuY93AaBHLv1IbPTHhAkTZDZues6mTZt269ata9euDz/8MBHFx8eT80wYKFGihLbO+Qj/3o3CggULdDPq1KkTHx+vjYFsCF1Z1QmcRpLhpGTJkrr98LAjolKlSsmjVahQgQ0CyWJijRo1AmyDL/BDDhHR+fPn2eA+PusvvviCmQ8ePEiGegvjECSwvEp5BfgXJrIzZ85MmTLF1LU33HCDv8zQiIqKGjhw4ODBg6tUqdK/f//ExMRhw4ZJ9/v1ag4fPty+fXvpoa+++oqMb11DD8dBMUEJxo4dq4mrq9aPrDUk1AvPAiJKSkoKvBkFwg8OuQoDIipdujQbjvEjRoxg5vXr1xPR6NGjWZmCKlSoQGqOSkQNGjR49dVX586da+pasIqIhg8fHm+gd+/eu3btGjFixCeffMJqLDty5Aimr+Ls4bbxzz33HLlTDoYPH466ZODD2GdytIiPj//www+ZOTc3FzcGhSIF4pNPPpE2fPDBB+xsWoPDODpl+PDh7PzFipAuhHb6J4dq1arVs2dPnOndu3fx4sXlAqyHoxcXLlzISjvGBeIj8d133xHRrFmzHnjggY4dO44ZM0ZXJN+QqQFYXXriiSfwa6lSpUqXLo3j9u3b4xq8X0zyZU2D1aDg+lw1atTwJNIeffRRZr506ZK+HotuhbMeLrpXlSpV2HBokYc6f/48KfkqwygiW4RGhdBOi3N7Dfk4TL5d2v1DzrDBIWauXLkyET355JO6tJYtW7rt76effhrnR44ciRh73Nu4cWP9Eq9cuQL3LllzYGOC4/aFvvnmm+QiYgcNGvTee+/JNeKNZHJlCTXEzAbbrPazYzVT07e8++67OHnPPfcUOTk0fvx4dLYnI4fb825N0hjmWYU5a4BYpCZxKAHpz7Zs2cLGeDds2DBmnjlzJqlRUv7qfxG4aKprwYIFcXFxwhuhEZRT1+fSZXoZy7QlwtM1rtfL5yefHJ5L2mPStMRgDYcQdpkwZmZmNmrUqGhxiAx1JxDg7QwePLhy5crMvGXLFteHxMI4GZM4SbobHR0tF4NPOJa0aF7GF+HQ2rVrU1NTRVMmov/85z9///vfydBM+/XrF+AziiOljxzSlneRMceOHUPzsMJowqxZs/Br69at2cU4Xr169fXr17Nhqg7wcXyBr3Xk5uaGQpG8cOGC6YzWXfQ4qAVJq1atKlWqZDrvZa0Dkk9QtWrVfv36ycxczvft25eDpy/7qDPluwuildVWneEEOHr0KH4C6UUpBKD7A/gaA3wKX+BTHXgdvstnTzhw4EBqaioRQY/GJ2vSLV555RUiatKkCf4FMzZt2nTnnXfKGyHlMEREEydOZK8c+vHHH/GKt27d6vpcpkEhQH35+++/b9q0KZbi/cLs2bPfeuuttLQ0mRXKbEtfJvQyoVq1au+//75+BC2tQwo/6vCLQ/rJDx48qIWt9/BTjFkSXihWytatW48aNeqPRisrOSlnK1lUMnWhyCH9LKwWTPTnG+B3Ir47cXFxKSkpKSkpsbGxsJdqQIoAJUqUECuiQKtlMhdr06YNfoUZ7LHHHouPj+/WrZtuvHTT3/72NzJUAkcwfNg9ISQ8LV++PA5mz569Zs0a09vp06fPihUrsC6Rmprapk2btWvXxsbGxsbGbt26VS5DcALe3S+//EJE48aNY8Mza+zYscz87bffEtHQoUNRXa1atapXr16/fv2GDRvq9rjVqdmgy8WLF4P47LBF+QitmWmIWqYnYsOGDcNitlslSQMvDXFwbFAwdHPJkHDo5MmTzIzRB8CSRfHixfX35wmYIpUqVYoNeQYbJkaiTZs2kTFBY+bo6GjRbObMmcPMs2bNMok6LIC7ckg03yD6jaDniCgqKmrAgAEQFQkJCY+5oE+fPsuWLWPm5ORkVqvRoh5pvwasB2DJBYZWkS75KnkXoCf/8m+EySHA4XA8+uijmhywerVq1eqhhx5i50BgkcBiB5JCcBlsfXhZkBxaPsvHeubMGTKs507P6Y5D+QaCOF344Ycf3NblF/JVFBH+NmnS5B//+AcRDRkyhI2Wm16dALc8+eSTRAQFIKR7W4WKQ7rFGRkZjz76qHYq8nKjOKKz8yqmFGuylAgRRblBWjR2Vg481at9S+QuMfCgq0BfhzNMH4B00rp161AX3D6lnZAueqbp9llk+iLWdmZevnw5yhQlSb9eaQ87T1AkHlee1MtrDwSFGue6fv36atWqkeHp4hZaDsHi7P0b0objvXv33nbbbevWrYODbIEcwvAhOUPkYpN4Q9eaArvYg/Ohp7p8B5yMHcrEjwKrVq3q5S5pDF4gM3fq1ImItm3b1rVr1wDloneEnEOuJFi6dCn0ALdAQkWylEpxy5YteIOuWifKDGKuIFn3PXTo0Jw5c44dO7Zw4cLk5GSRQz179kxLS3vbAOYWiYmJZISuuqJkyZJw58C0FC9NQsy8ZxrJNxyFYbl1RbAe3BUh55Apm0KB18M+RERnzpxh5jfeeOPEiRMLFy582zMWLFhw4sSJ6OjoxMREOAiUL19eK+/iZ9OlS5f09HR9b3Jy8vLly2GSWb16NfzXEhIScD0OMCHQ7koovGTJkp6mCL5MHbwAlgsthOCE72U8kqTKrGS5LOCIWSQUKNRYacG3337r9vzRo0cRPIU+gBD2Bf369ZNjtz4qXs4HC9rGg/bXrVt39OjROFOnTp2hQ4diXYWIhgwZAp2XjJk8gmHQSJPrOhmBVj6+dphI9POajKvBRajkEIykRLR27dq0tLT27dujm0uWLIl3XbJkydKlSxcvXrxYsWIlSpTAX1MflCtXDiflszZ938WLF5eeQ1Hyky5N5NCoUaMk4GHIkCH9+/cXF4CoqCjp76ioqCFDhmAljow1ELiEk+ELhhVNcTrQP504cYKMMBh2VvPxVWDlMS8vj4zwGG2DdcshfyPFEMmJlwDfwAizDzEzdGdrcDXaEtHIkSNlZpeQkPDpp59KHw8dOlQs0ehFRPvfeOONfzykkamDmU+dOqU7FeEDstCBQnA8f/58UiFQEJBi0dZX5uTkkLGAIz/h00fWqU8//ZSZs7KyyHAGYsPL5euvv8ZIev3118u92lfd9YwvGDNmDBmiCDOYyJuXwcuOiOrWrTtgwACR23Xq1Bk2bBg+4qpVq2KFWXc/nGYkGJmc10Z0z0lMBRuzX3iDsLsOnjRpEv5Fz8FMB6fe6667Dj/Nnj2bDI9BKWTbtm1sLJXLlViQwXqWqf24UrdESANXJ6jG8Bi+6aabWCVMZndSxxqHWLmeij02RAihPtSsWTO96KPflAQPyU94m8z84IMPyk+//fYbKUMAJAF6Dl58whVNGiwgmPiEDoazutSl78K/IrowPYRowYqK6UrTv7LeQkTwbGHmbdu2CV/xE3azZ+bly5d37NgRfJ0/fz5OStIqCcNCCf5yCO9/5MiR0k5XO2QQESo5hCEDr0/CDPATRLrQC6kwIO1xpfyk70IMuQQqyE+yDIkMnuxMVvwrAgO5XVEXftLhEG3atJGhauXKlR06dJBVlOjo6PT0dDa659KlS2J4ZEUCZn777bdxF2bacMF2NQnKv1BTjh49qkPVJEEKW5JDUj4RVa9enYMXruQWIeEQBLV0P6br0sdQldjoubJly8qVkvSembdv3y534cr7779fComOjt6wYcOcOXMgLTp16sTGS0f6JjZepbgowfiLTtVrJuzs665NyaafTGZGQNbatBnMoby5xUImqY/E4wwHklDm9ttv1z6sem7vL4fkXgyLrmtqQURIOPTee+9VqFDh2muv/aMOonLlyrHRczDSyMVr1qzBoiMz5+fny1oYG93vxbUUI86bb77p9jLdwdqNROf61Gsa+SqeVdbRhCiu7BG4jeY2HWi7s8TOYgGkRIkSMoYuXLiQiOrUqcPOHPJ3XuYwrPOHDh1izyb1oMBXDm3atEkmL/4Cn76sJ+ifTF3u9lifcTivRcDZXtI2sBopNmzYgDOe6tUFavnBKt+SCBJTq0xklStNS6Gaqa5PIVi1atXKlSuZ+dy5c2BM586dWfFA5JDbD8kt5F5JBuL7vf7CVw6dO3fu3LlzPl6sm4tAs6CvG4MZcPhy+43CzG3t+5M37qP8l7FJ/tViT9wL3UIkpaxpSLgPpJTmkL8+Kpp8YeaQfjs+litiAFMMk5IRIERD3LFjhyddweEcJuEXcIuMsL63JyYmZs2aNew8XJ47d857/0mQxuDBg+fNmyf6kNapoWX7+yxE9MYbb3BR0Kn1SO9juWfPnmUjwE+UCcutNEG6JzMz05McggJrTYZrHwxfrtebGLHKNSg+bt77jwwDIytpJHdJFKXv7dEly43h16ktkMCtwhEsSIFENHPmTNcqpF5rVVt7WGtFSQg2DGCm1AAIpkPSFQtySIoKvz5UZCGvqSjkQbMAiAfxMnPlkJdA7wJh+Ub/agl1BaGGaSYciRD2fP75567pBnRAgb/jkc0hn0DOESCRiDJlytx4443IgiUZF+RXm0MhBxkLtBHKIa2mIKDA1PF6LPNRpxGRbCrq+++/37dvHzPPmzfvnXfeWbRoUXZ2tk5vZw1XA4cQ8xo6nbFwYNqbTM5b0IdkXilbHAHkAQG2/GrgUCFvtRR0LF68GH1Zr149cXSUXy1wSKxBphtjY2P79OkzePBgImrYsOHjjz8eFxenY3yt4Wrg0A033MCRr1PDKotVZN3x06dPtyAt8DawOY7bGr3vcOIXIpJDsibKzEQ0a9YsVguZIV1ftAxZUHMrL8W5AO5TRPTBBx+88847SEwoHPL9udxyCFVj564groFEJIf0IgYZjo7CnpDGlgcIV37LSuKxY8c6duwIuri6jfvFIU86Nc4/9dRTZCQvCMoaVERySD82GUtCgC9rC2EBXBYlHlIA0yjYU6dOHSTrcMX//d//sc86n6xsSMo5AFXDnQteGEFZz49IDjFz06ZNjxw5wsxEFBcXB59RRFkUWs5Nv3D27FnxDDH9BD26UqVK//73v+E/RIbD7qVLl/Ly8n7//Xdc6fvesXgDpjRWoIt4G0v4doCPFqkcwosuV66cfKmmMPvwNs8T3DZs0aJF2AqSlT507NgxH293hdCidu3aZPhXicgxDXB/XjkkIckIMSYjvjjiIKLl+PHjyDGK9TKJSbKwDihaF6L8MHvXGqS/szzviEgO4V1UqVJFq5+B2znCAlBEkllB4SWi5557jq3qvA7DCRi2JTY0d5wkw1E/WIhgDmG3RsBLIpGiD6yImaJZ4Ltn2U6Bu+ArjDPQw5CaEhksg4VI5RDekWznbjkngXZa9QvQuiz7+GoTV3p6eqtWrXBeNu7UjnX5aqsuXwoXtR3sfOWVV+SnpUuXxsTEwH07WIhsDkniOmvlwNsVXogW2mB5j3MxQOhpmmww5Zq2ARYBV7uAJ8jMFHEvErMQoqlGRHJIdlNgpSFak/mB2LXzA9h3AYFy0tkifiTti0kO5avsej42jI2YBfE3zzdiB4Jrg41IDknkDTNXrFhRYpP9hYT+WOAQbIaWv+zTp0+zMSnDzl1EpLMPaA45nKOdCoRYNz777DPNIVNcW7AQEIckhKqQbXoYfVDp+vXrBw4cyF7lUL5z7kSTv713Hohftql8xB65vV7HFTmco8y07UoO0tLSihUrBgKxZw55qtHt86J22BiFQ748sjTS9z4NiEOS6L6QOSQrYngXFy9e9K5vSoSyMM8vG7/YV3y5GOMsBh0E9uPGlJQU9hpnl5OTo3N2BbI1vdSCJAV+xVnn5eXh9RYSh+SDC5ddWNfrF499/84cDsepU6f8LZ+ZP/30UyTwdxi5Xd3Wi19XrFgB6owYMSJwDsmngkTHfnEoX8Xs+nhLoPqQ5OcOsBy/8OOPPyYlJf3444/MnJSU9O677+rMG66QfVLIyInGPqsy/u4DBKV4ypQpf/nLX6QEGT3d6iLiMY3MMkHhEFqL5VV/OcSGtucj/Isv813e4GJr8TpQHt3WRc7Qm+IiOYFugAjIxo0bV6pUKTExsWbNmjKPC2IEmUZeXt758+cdDsfx48fZ+b15KiE9PT0mJmbVqlXMvHLlSrTQ3wB7U1Nx4969e8lwN/Nd7rKh8osNTLRetxzwiUPbt29n5zQa3iFO8tY4hJ2HTd+rzOTr1q27a9cuRH/WrFlz27Zt+NpMuzwLgWbOnGlKpUVq1TrskFeUlZWF/MOwD0lqWAsyPt/IM7xnzx4y/Kus2VGh3jlU0hJX+MSh6dOnsz8cOnjwoDTCt9Y6Yffu3R9//LHrecReYSEJibB27tzJzhZ9gUMtD2kDEqk9ry20LehAMyTjR4MGDXCAHYytrZfJXSClFGWhHFMP7tq1y3VPel/HMgtzeL/mPhrz589fsGCB63lk38UxrGc4lpVFU+04EEOtw/B8aNmyJRcZDkmrxD6EYAzhfYDtJOeM6RbaNnnyZKyywQ5Xt25dcxX+lujX9Zbb7RbyZtmZN/Ba/+GHH/TFMpaR2ngam57279/fe0WFCZGOUKhzc3NFw8MFFtq5b9++t956a9myZdhjKS4ubunSpcwMEeJ7v+AybOSlrVMmu2Ak2an1m9UySZ8/ePBgdHT0Aw88wM55xPDrfffdF0jfhAIYcOGTLyMa8vNbLvPaa68VIppcs9kfex4uW7Bggd4SdMeOHayWgTlyOWQ6lulrkyZNoG53794dZypVqkRE5cqVK1++vB4jigiHoDJnZWUhS3XdunWbNm2qn84acnJymHn37t1S1G+//cb+6yTNmzePi4vDuwLdkWUFiGwO3XDDDZpDOp353r179Vamn3/++S233IJ7TSk1igi+++47NA9TS+RWD0o7+/TpozV0dvY58QVEtH//fnY2ATZq1Ag7a/2hLQTe0EJDy5YtZcOhVatWLVq0CMdz587FAR4pOzu7RYsWgwcPxsnk5GQxHRERzvvuR1E4aNeu3YMPPshGRvYAOZTv7DpNxoZJFkTvhx9+mJCQgONBgwa98MILGRkZZcqUQYaJCJND0uV6GHKoBVSH4YZxzz33lChRAnMcJCju0aNHYmIiNq8w3Rh2aHPJ2bNn0eW6qRaAR5s7dy6KgkoEm6e/+Oabb2bMmDFhwgRk9sVmuv3795fQIo4sDukdTLXhC8ZM2Ax//fVXeft4Qji6E1GlSpVWrFjB/svzkEJagi3ratasGaBjHTtPJmQrnPvuu8/fcvBN3nrrrXKmefPm+oI/LHCWG1rIkMVkceSQxOFaT0RCAukDSKycnBzYvllNKIpILKzub8wD3nvvvcD1oZMnT8qkTLZTstw8fSwiP/Lm9t6XnOSny5cvX7hwIScnB0lFTbYQX1avChloRrNmzbCwjy1KAucQIu31TIJUkh2/1j1dj00lRAyHrlZoiSgSKEB9iJmJqEuXLsyMZWZmTklJadu2LYfArmFzKMwQS92qVauIqHr16rJPV1DKN4VLizIQlMIBm0NhBroTWYVlf7Sg6NSYZMCpgY3FH4fyzQ0WbA6FGaJTlylThl3sQ9b626F2LWrevLlML0KkAtocCjP09FAvuAqHLJQJvx/cC+daDqWvqc2hMEMkTbdu3YioWrVqJn0Ia5x+wWFslsXML7/8ciB09AU2h8IMiIdnn32WjF3emJmIJHpaZ+jyEUKXQ4cOwXEPKYVDBJtD4YcsTbDzcPbll18GWCYRLViwIFhTPE+wORRm6FWX1atXa6sgXJAD9GGFo7BsMhwK2BwKM4RDWNerXLnyF198ASYhPMiaT7645cPhMzMzM9gN/x9sDoUZIBA0X1MKIsmB52+ZYA/+ouSxY8cGs9HOsDkUZkDMvPPOOxKGgAkaBRZiJjdiLNOpP7z7wuolVR8rsjkUZiC+Xf4FgbDeHkioq2D06NGkotXE08HT9eIf4fsYanMozJDuFAe0kSNHajkUOEilQvNrl2Nfy7fSKBvBA4YMBHCR4VIdRA4hTLFXr15r166F9/CiRYtSUlJSPcPf+aDNoSKB1NRUIkpLS8O/XjgkXYvdYcqWLXvttdfiLw708XXXXUfOQCyDdwwZMoT90cNsDoUZEh2APpOsjF7kkHZ9tIZ69epVrVr18ccfv/nmm+vVq0dENWrUGDJkCH6NiopiWw5FELSGKzMyLxzCeiozN27cmIgaNmzYs2fP1NTUK17Wv0MAAA5uSURBVFeu5OTkXL58OS0trUePHoiaBRBrBuTm5opbsAA+n2wkvrHHsggDxM+hQ4fAG7gQIT7OE4dwC7KhI+jHhIyMjPfff3/9+vW9evVCnDgs4F27dtWXafkHwCDZoUMH9ic//1XOoaITA+QdqampJUuW7NSpE/7VcsjUfnmidu3aEdGkSZPYZdJuGrkqVqwox0lJSbook2v52LFjkc/Pr8ZftRxatWoVAhqLiO+9J5iseVlZWQ899JAXDonlBvpyTEwMM1++fNm0mwIRrV271nR8xx13kNf8Xdb2sL5qOSSpBYq4HJLQyuzs7F69emn5gR2fPckhOEoLJyRSipmJ6JlnnsH1puMxY8Z4aYzmkD0v46ysLC7a+1ABwnJ0XlxcHDNHR0cTUaNGjdgdh0AUvVewzpJ77NgxInrqqafkGDm7UAUW8D19V5pDfujUEjMaxHct70WPuDo4tXD6tUgRSIdT6vNypnHjxjhz4cIFUuklXDmEA3CoXr16unw2wplxEnq3JOgkY/0EhXz//ffsPDHE4prf+tAVA0HMT4g2ISQbTWeXQNVg1RUp0GONhsM5Q6Ge3mMrRU/zI5PMEL0K21jhmkmTJskx5nrYHEeGPKyByPiI/T3IT79HCkWecjzMyZMncXDp0iX9+oq+jhIigC6uz463dOLEiR49ehDRbbfdBtsPEiZ70m1NHNLKkPCmbdu2cmza2xXetxjmxPka11iZl23evJmD6rMtb0rogr+PPPIIF9X9VkMNpB91tTWg87Zu3UpEZcqUSU9PZ2Y4sHrXbbU+pDWEBQsWiBsJEcXGxuJ4xYoVzZo1020gF9eALVu2oExk+PcRxMzZ2dle2uoFOlkCbh80aBBGWV2g6CVIxWWtLo2gK3CFgLlz54IfJrkiD4JeYGOVtEAOaTkkRbk9Zue+kJNDhw417aKMTA/kZ6KZgOZl8kmJ0WLbtm2SxC50iNzR0NW3S8JP8a9kuilwTBEOIXu4Bdx9992ya6yosChzz549vpcT6Nw+MTHx888/l3acPn1ar86ECHjgjz76CANERMDTnFQnYYE+dOuttzZp0sR3DrFVPaRr166DBg3CMTR3ZEolIt/3ueLAOZSTkwMhXJizLRH+J06cKJwaA4foiKZ5ltZOyAgx0/qQJ7iOZYED9iQi2r17t+93/RHEFLieK3YgE5M++eQTdklHqi+DRm+hrsiCW42E1bfXsmXL6OhonPQylsloCA516tRp48aN6enpKxTSDci/+mR6ejrGrPLly5cvX75s2bJEJMEkBephrqAGDRpwKOdKyEgq5WdkZGAlWWgEg/KfFia7kc5h5ZZDoguKHAoF2N+1DocKzw4FJO+dVCHGxghVjYMIvTMOPDTi4+Pr16/viUPyGsXt2gtq1KiRmJiIhN0ouac79OrVS/9Fhng/OCQdbG2PnwJhSsSJfBSiYBa1HL9hAXqrTZs2RDRgwABmnjFjhicOyeeXl5d39uzZ8+fPI9tkjjPOnDlz7tw5uYvUyqsv8Ovz/l+u3RDJIb1kxs5qkz7zZwbewNSpUxcuXIgzWK8gI7+4p1t8L5wM70Tvl1mr4qpdt48U4FsSfah79+5IxhislP6uCyBBh82hMENvwAv7UJUqVbDeTkQWEseYIHJo3LhxQWiuO9gcCjPE5IFF0LJlyzLzsmXLwCFs+BcIxPiEvRxCAZtDYYbMMHJzc7GL6pkzZ7p06QIOWQuXdtVuiahatWpBabArbA6FGabN5CWHFfSh8ePHWyuTDUeOfv36bdu2rWPHjkT05ZdfUghyEdkcCjO01wO2MCMiCRd0u69tgRAzzfDhw12NRtgNJ4iwORRmyKQM+tCNN96IcBT095w5c6yVCVJ+8MEHZGwdBMEGP+vg2uRsDoUZYsHPzc09deoUTkqAB9JY+QutD910001aCCGuw+bQVQWTPnTq1KnevXtLlz/77LMBlj9x4kQiKlWqlBicHO7cugOBzaEwA+xBp/bs2RPUeeKJJ3CwZcuWAMt///33hZEykAV3bcDmUJghLqAQGESEjfpwLNkUAgEyMchAFvQ1SptDYYaIhGXLlskuhQgxI6KRI0cGXoVYvV0rDQpsDoUZWCEXBeXYsWOYTAEfffRR4OWzvV52dUPr1BLRgbxSRCRbZlsGbEWJiYk2h65aiKfO+PHjYR/CppxBXC/Lz8+/dOlSENrqATaHwgw9S7rrrrtwIMOZ7+tl4tDncE5twMZw5kWPFidBt9cU6ONqcyjMcLUP9evXT/ShoKSoloo8/aSDln7++eeUlJT09PSVK1cmJyezs7euW9gcCjP0etm6detAnQEDBtx9993kz/ro3r1709PTN2/eTESlS5d+7LHHdu3aRURlypQhoiNHjnhvA5qhd3EEJKmDl9ttDoUZMinDehkZGYaR027atGk+liMT+FtvvVUYkJCQAPUc1kVP0En4qlSpkpqayoZChtygNoeKNPTaVvPmzRcvXoxjSSTtYzlI4YDU0vD6gHv/1KlTyUgZ46UNzJyUlERE27Ztw0mpvUBjks2hIgeIBKR98Z1Db7zxhlyMVFQ4Rkoh7/eKvyyuRCYqzSHvdm2bQ0UICJxCh82fP79s2bK+O7Bqwk2bNs312AsPTHZIE6UKjBOyOVSEIFF4ejbu47oEEVWuXNntMRWU51Vnk8WZWbNmkbG+VuA+VDaHihC0buQpf4GG0OLEiROk8p0TEULU2VmcMHNmZuY333yjq2AleFq3bo0zHTp0IKLRo0ezzaGrGzLKjBkzRhTn7OxsUo7YQgVm/umnn+Rf0CI6OlqGy4EDBxJRuXLlxIMW52196GqGcEjnWhwwYAARrVmzBv9qDqWnp5OxfuJ2Lfb6668nolq1apmUIZtDVy1klElLS5PUxBcvXkQqFXR8VlZWbm6u/DtgwAC38/wjR44Q0YULF5j50qVLRIT0Vr7sqWhzKAKgV8H0ee9B8m6VmJEjR0r+PA0MZMWKFatatappIPNUlMDmUARAJEHgftBPP/30Pffc4/YnJLMioh49emDHRR9hcygCIF70gfsfDh061NXkKOrOyZMnJT2hvefLVQV0J1bRA4HD4ZD0zhquWyQUuFavYXMoAhDqFE0OZ/h+1x+Tu1C2zcbVif/+97/a9m1zyIbfyM7O/vnnn1mMTOFuj41IhcwWbQ65gcxTQpTntChDjIoFxjGK8mRzyD3+9a9/9e/fP9ytCAOEQ3ZOz4DgcDhOnDhx5syZcDckbPArJt/mkBvI6/sT5s4WK5TNISswBWe5BTt7ivkl83VFsrdrXl6e2xJQMjwbTffmO29+EiLYHPIbiPOSMD+3MHlBuF0H9bEuVxKY1hYkHz4zHz58OC0tbdWqVUuXLpWqmfngwYPp6ekZBlavXr169Wrx6i802Bz6AwV6yWgcOnTo0KFD7IN/llvI+tfy5cu3b99ORMeOHXNtD4jy8MMPk0Lx4sVlvUL89k3wtz0BwubQH3AYO5ZgT9MKFSpUqFDBtXsmT57Mzk7KFtbStdM7MHDgQLfX9OnTh4j69OnTvXv3Rx55RLNk//79RNSpU6f8/PzTp09fuHABEdaBh+j7C5tD/4OMSuIMumzZsvPnz2dlZZ07dy45Ofmaa67BBqgzZsyYOXOmvlE70heoJ+EnxJ56khyyR0KpUqXk5Pr16+X63NzcKVOm6FuWL19e+EKIbQ65xcsvv+y2a1NTU7W2IXpSIG49qAjZzTXASIlxhoxEGKFumFb2wzKQsc0ht9DbXErWi3379ulrsP+3yJtff/01JSWFiPr27btx48ZVq1b56KqBimRfVYF2IBRdDcGHkEyQdnrfMAzBAT67BdgccgO3W6WSEXxDRDfffLP+FanvZs+ezczly5f3S7f1dKWMjHo+2LlzZ3Le0F4WrWbPnk1EW7dutfzUlmFzyA2EQ4MGDXrssceIqGLFiqKuOhwOU8frfydMmEAF5UjQwL1YBtfQcgh/z549K0JINDAZSbGbAofe2cjNIxRyfREB4VDFihXbt2/frVs3ZAp/8cUXcYEXDuHfiRMn+liXLxILtGjdunXp0qXlzOXLl3XuIimn8G3rNofcYNSoUa5dW7Vq1cGDB+PY9Ot1111HRPPnz2fmy5cvU0F5NjSkKO+Ked++fWWoEv98HUxNRMOHD2ebQ0UH6NovvviClVH44sWLbmdA27Ztw5ndu3cT0TXXXONvRd7zDP3+++9ElJGRIWeSkpJY2SoxX9uwYQPbHAoj9MKFzO0/++wzdjZG64Hjtdde02cSEhJiY2Mlx7SXOb/eZRtFYZSUilatWhUbG4uLL168SEQxMTG7d+9eu3btzp07r7nmGlJBqKw4XQjraK6wOfQHMIcXpzOtXojmwYZMql27NhHt2LEDF2OgOXDgwMaNG5n5l19+wUoIG7u3wLot0JGjqKhz585s0HHnzp1S+9GjR8kdkJ9KK0MVK1ZkP1dsggWbQ39Ar4NCpyGifv364Vcddp6VlYVfExIS8KvuXVkhwRIYjmHdFojA0zdu375dLmjRosW9997LzIsWLWrbtm2XLl26d+/exUCrVq1wmYi6u+66a/Xq1RzK/cG9wObQ/4C3n5mZqbsWmeohpcAhhBXHx8eLSjRu3Lhq1ar16tWrS5cuHTp0iIuLq1atGlK6XrhwoUGDBq4VoahffvklOzv75MmTx48fl/Miorxr2Q6XhMB6ql+YsDlkBnr01KlTp06dQteys9HlwoULR48eZSO0D2IJupEAi+2eqnArLeSk6UDD7cWmQqw8c2CwOWQR8vVjgVZPrE6fPk1EiYmJYWpaYcPmkHVAH1q9ejVGPeQ8mDdvXps2bWAr+pPA5pB1nDx5Ege5ubktW7bs0KFD69atxdXwzxNX5DeHHMrjOBQNiiy4fQl/tjfjN4eg9he4D4iNPw+sj2V/wrgZG27x/4ujgtUV287SAAAAAElFTkSuQmCC)
3. When the plane is a smooth inclined plane, as shown in Fig. 1.28, then
![Acceleration and Tension in string of bodies on inclined plane over pulley Acceleration and Tension in string of bodies on inclined plane over pulley](data:image/png;base64,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)
4. When the plane is a rough inclined plane, as shown in Fig. 1.29, then
![](data:image/png;base64,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)
3. When the plane is a smooth inclined plane, as shown in Fig. 1.28, then
4. When the plane is a rough inclined plane, as shown in Fig. 1.29, then
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