Physics - Rotation Question with Solution | TestHub

Since the two bodies have the same mass and collide head-on elastically, the linear velocities get exchanged.
Hence, just after the collision $B$ will move with velocity $v_0$ and $A$ becomes stationary but continues to rotate at the same initial angular velocity $\frac{v_0}{R}$.

So after the collision, the kinetic energies of $A$ and $B$ are

$K_{\mathit{B}}\mathit{=}\frac{1}{2}m{v}_0^2$

$K_{\mathrm{A}}=\frac{1}{2}I{\omega }^2=\frac{1}{2}\left(\frac{2}{5}m{R}^2\right)·{\left(\frac{v_{\mathit{0}}}{R}\right)}^2$

$\Rightarrow \frac{K_{\mathrm{B}}}{K_{\mathrm{A}}}=\frac{5}{2}$