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Q.

The two pulley arrangements shown in the figure are identical. The mass of the rope is negligible. In (a) the mass m is lifted up by attaching a mass 2m to the other end of the rope. In (b). m is lifted up by pulling the other end of the rope with a constant downward force of 2mg. The ratio of accelerations in two cases will be

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a

1:1

b

1:2

c

1:3

d

1:4

answer is C.

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Detailed Solution

For first case,a1=m2−m1m1+m2g=2m−mm+2m=g3    .......(i)For second case,From free body diagram of m,ma2=T−mgma2=2mg−mg       [ As T=2mg]a2=g           From (i) and (ii) ,a1a2=g/3g=1/3
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