Physics - Center of Mass Question with Solution | TestHub

Initially, the body is at rest, so its total momentum is zero.

Let the two pieces of mass $m$ move along the x and y axes with velocities $v\hat{i}$ and $v\hat{j}$ respectively.

The mass of the third piece is $M-2m$. Let its velocity be $\vec{V}$.

By conservation of momentum:

$m(v\hat{i})+m(v\hat{j})+(M-2m)\vec{V}=0$.

$|\vec{V}|=\frac{mv\sqrt{1^2+1^2}}{M-2m}=\frac{\sqrt{2}mv}{M-2m}$.