First slide

Rolling motion

Question

A thin hollow sphere of mass 'm' is completely filled with a liquid of mass 'm'. When the sphere rolls with a velocity 'V' at center of mass , then kinetic energy of the system is [neglect friction]

Difficult

A

$\frac{7}{10} m v^{2}$
B

$\frac{5}{3} m v^{2}$
C

$\frac{1}{3} m v^{2}$
D

$\frac{4}{3} m v^{2}$

Solution

$total kinetic energy of the hollow sphere \frac{1}{2} {mv}^{2} (1 + \frac{k^{2}}{r^{2}}) = \frac{1}{2} {mv}^{2} (1 + \frac{2}{3}) = \frac{5}{6} {mv}^{2} kinetic energy of the liquid \frac{1}{2} {mv}^{2} total kinetic energy is \frac{5}{6} {mv}^{2} + \frac{1}{2} {mv}^{2} = \frac{4}{3} {mv}^{2}$

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