Question

A massless thin hollow sphere is completely filled with water of mass m. If hollow sphere roll with a velocity v then kinetic energy of sphere of water is

• A. $\frac{4}{3}{mv}^2$
• B. $\frac{1}{3}{mv}^2$
• C. $\frac{2}{10}{mv}^2$
• D. $\frac{5}{6}{mv}^2$

Answer 1

The correct option is A $\frac{4}{3}{mv}^2$

Kinetic energy of rotation -

K= $\frac{1}{2}I{w}^2$

- wherein

I = moment of inertia about axis of rotation

w = angular velocity

$E_{trons}=\frac{1}{2}m{v}^2+\frac{1}{2}m{v}^2=m{v}^2$

$E_{rots}=\frac{1}{2}I{w}^2=\frac{1}{2}\frac{2}{3}m{v}^2\frac{v^2}{r^2}$

$E_{rot}=\frac{1}{3}m{v}^2$

K.E of the system

$E=m{v}^2+\frac{1}{3}m{v}^2=\frac{4}{3}m{v}^2$