As shown in the figure, a small body of mass m is placed over a...

Since all surfaces are frictionless, there is no external horizontal force acting on the system comprising the small body of mass $m$ and the larger mass $M$. Therefore, the horizontal momentum of the system is conserved.

Let the initial velocity of the small mass be $v$. The initial horizontal momentum of the system is:
$P_i = mv$

When the small body reaches the vertical part of the larger mass, it can only move vertically relative to the larger mass. This means its horizontal velocity must be equal to the horizontal velocity of the larger mass. Let this common horizontal velocity be $V$.

The final horizontal momentum of the system at this instant is:
$P_f = (M + m)V$

By the principle of conservation of linear momentum in the horizontal direction:
$P_i = P_f$
$\Rightarrow mv = (M + m)V$

Solving for the speed of the larger block $V$, we get:
$V = \dfrac{mv}{M + m}$