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Question

A stationary body of mass m is slowly lowered onto a massive long platform of mass M (>> m) moving at a speed 4 m/s as shown in the figure. How far the body slides along the platform?
[TAke μ = 0.2 and g = 10m/s2].


A
8 m
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B
12 m
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C
6 m
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D
4 m
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Solution

The correct option is D 4 m
Draw the free body diagram of block and platform. As M >> m, the acceleration of the platform, a=μmgM can be taken as zero and hence its velocity remains constant as 4m/s. Acceleration of the block is, ablock,ground=μg=2m/s2 towards right.
Let velocity of block wrt ground at time t be v (towards right), then υ = 2t.
Solve the question w.r.t platform frame of reference.
ablock,platform=2m/s2 (towards right)
υblock,platform=(2t4)m/s (towards right)
Initial velocity of block wrt platform is 4 m/s towards left.
Let s be the required distance, then v2=u2+2a.s0=(4)2+2(2)ss=4m

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