Q: A thin hollow sphere of mass ‘m’ is completely filled with a liquid of mass ‘m’ when the sphere rolls with a velocity ‘v’ kinetic energy of the system is (neglect friction)
Sol: Total energy = KE + rotational KE
$\large = \frac{1}{2}(2m ) v^2 + \frac{1}{2}(\frac{2}{3}mr^2 ) \omega^2 $
$\large = \frac{1}{2}(2m ) v^2 + \frac{1}{3} m v^2 $
$\large = \frac{4}{3}m v^2 $