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 $\mu$ = 0.2 and g = 10$m/s^2$].

• A. 8 m
• B. 12 m
• C. 6 m
• D. 4 m

Answer 1

The correct option is D 4 m

Draw the free body diagram of block and platform. As M >> m, the acceleration of the platform, $a=\frac{\mu mg}{M}$ can be taken as zero and hence its velocity remains constant as 4m/s. Acceleration of the block is, $a_{block,ground}=\mu g=2m/s^2$ towards right.
Let velocity of block wrt ground at time t be v (towards right), then $\upsilon$ = 2t.
Solve the question w.r.t platform frame of reference.
${\overrightarrow{a}}_{block,platform}=2m/s^2$ (towards right)
${\overrightarrow{\upsilon }}_{block,platform}=(2t-4)m/s$ (towards right)
Initial velocity of block wrt platform is 4 m/s towards left.
Let s be the required distance, then $v^2=u^2+2\overrightarrow{a}.\overrightarrow{s}\Rightarrow 0=(-4{)}^2+2(2)s\Rightarrow s=4m$