Answer: A
Considering the origin of the coordinate system at \(4m\), we evaluate the position of the center of mass as
\(\dfrac{4m\times 0+m\times r}{4m+m}=\dfrac{r}{5}\)
Thus the center of mass is \(\dfrac{r}{5}\) from \(4m\) and \(\dfrac{4r}{5}\) from m.
The ratio of their kinetic energy is given as
\(\dfrac{\dfrac{1}{2}[I\omega^2]_{4m}}{\dfrac{1}{2}[I\omega^2]_m}\)
As the angular velocity of the both the masses would be same we get the ratio of kinetic energy as
\(\dfrac{4m(\dfrac{r}{5})^2}{m(\dfrac{4r}{5})^2}=\dfrac{1}{4}\)