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Q.

A thin hollow sphere of mass m is completely filled with a liquid of mass m. The sphere rolls without slipping. Velocity of center of mass is v. Kinetic energy of the system is equal to

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a

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

b

$m v^{2}$

c

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

d

$\frac{4}{5} m v^{2}$

answer is C.

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Detailed Solution

KE = $K E_{s p h e r e} + K E_{w a t e r}$

= $\frac{1}{2} m v^{2} (1 + \frac{k^{2}}{R^{2}}) + \frac{1}{2} m v^{2}$

= $\frac{1}{2} m v^{2} (1 + \frac{2}{3}) + \frac{1}{2} m v^{2}$

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

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A thin hollow sphere of mass m is completely filled with a liquid of mass m. The sphere rolls without slipping. Velocity of center of mass is v. Kinetic energy of the system is equal to