Question

A small block of mass $m$ is placed on a body of mass $M$ at rest. If the block is set in horizontal motion with velocity $v$ as shown,

(Assume that the small block leaves from surface of $M$ vertically at A and all surfaces are smooth)
Find velocity of mass $M,$ when the small block leaves the surface of $M.$

• A. $\frac{Mv}{M+m}$
• B. $\frac{mv}{M}$
• C. $\frac{mv}{M+m}$
• D. $\frac{Mv}{m}$

Answer 1

The correct option is C $\frac{mv}{M+m}$

When the small block leaves the surface of $M$, its velocity towards right (along $x$ axis) equals the velocity of the body $M$.
Let it be $v_x$
There is no net external force in horizontal direction, so linear momentum will be conserved for the system
$mv=(M+m)v_x$
$v_x=\frac{mv}{M+m}$