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Q.

Atwood’s machine was an apparatus that allowed a direct verification of Newton’s second law. It could also be used to measure g. Two blocks of equal mass M hang at either side of a pulley (see figure). A small square rider of mass m is placed on one block. When the block is released, it accelerates for a distance H till the rider is caught by a ring that allows the block to pass. From then on, the system moves at a constant speed which is calculated by measuring time taken to the fall through a distance D. t is the time for which it moved at constant speed. Then find the value of ‘g’ in  m/s2,  assuming ideal small pulley. (The diagram is not drawn to scale) 
[Given : M = 4 kg, m = 1 kg, D = 2m, H = 1m, t = 1s]
 

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answer is 18.

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Detailed Solution

(m2M+m)g=av2=0+2aHD=vtD2=(2aH)t2D22Ht2=a=g(mm+2M)g=(m+2M)D22Ht2mD=2, M=2, H=1t = 1 sg=(2×4+1)(2)22(1)(1)(1)2

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