A stationary body of mass m is slowly lowered onto a massive 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  $\mu =0.2 and g=10m{s}^{-2}$ ].

 

for both M and m force acting is frictional force $\mu mg$. For M it is towards left and its acceleration is $\frac{\mu mg}{M }$ which is negligible as M>>m  so its velocity remains constant

 for block m frictional force $\mu mg$ acts towards right and its initial velocity with respect to M is 4m/s towards left. when it stops relative velocity with respect to M will be zero

$v^2=u^2+2as here v=0 and a =-\mu g = 0.2\times 10=2$

$s=\frac{u^2}{2a}=\frac{u^2}{2\times 2}=\frac{16}{4}=4 m$