Question

A massive platform of mass M is moving horizontally with speed v = 6 ms${}^{-1}$. At t = 0 a body of mass m (m << M) is gently placed on the platform. If coefficient of friction between body and platform is $\mu$ = 0.3 and g = 10 m/s${}^2$, then

• A. The body covers a distance 3 m on the platform in the direction of motion of the platform.
• B. The body covers a distance 3 m on the platform opposite to the direction of motion of platform before coming to rest.
• C. The body covers a distance of 6 m on the platform in the direction of motion of the platform.
• D. The body covers a distance of 6 m on the platform opposite to the direction of motion of platform before coming to rest.

Answer 1

The correct option is D

The body covers a distance of 6 m on the platform opposite to the direction of motion of platform before coming to rest.

When the block is placed its initial velocity with respect to ground will be 0 and if there was no friction between m & M then it will slip and go leftward so M will try to oppose its motion so there will be friction in the rightward direction on m by M.

$\mu$ mg = ma

Since M >> m, the velocity of M remains unchanged after m is placed on to it.

Acceleration of m,

Acceleration of m,a=$\frac{\mu mg}{m}=\mu g$

$a_{mM}$=a-0 and initial relative velocity $v_{mM}=0-v=-v$

hence s=$\frac{v^2}{2\mu g}=\frac{6^2}{2\times 0.3\times 10}=6m.$

Hence the correct choice is (D)