Physics - Center of Mass Question with Solution | TestHub

Concept:

This question is based on the conservation of momentum and conservation of energy.

Solution:

Let $v$ be the final speed of the system.

By conserving momentum:

$m{v}_0=(m+2m)v$

$m{v}_0=3mv$

$v=\frac{v_0}{3}(1)$

By the Work-Energy Theorem:

$\frac{1}{2}m{v}_0^2=\frac{1}{2}(m+2m)v^2+2mgh$

$\frac{1}{2}m{v}_0^2=\frac{1}{2}(3m)\frac{v_0^2}{9}+2mgh$

$\frac{1}{2}m{v}_0^2=\frac{1}{6}m{v}_0^2+2mgh$

$2mgh=\frac{1}{2}m{v}_0^2-\frac{1}{6}m{v}_0^2$

$2mgh=\frac{2m{v}_0^2}{6}$

$2mgh=\frac{m{v}_0^2}{3}$

$h=\frac{v_0^2}{6g}$