Question

A thin hollow sphere of mass is completely filled with non-viscous liquid of mass m. When the sphere roll on horizontal ground such that the centre moves with velocity v, the kinetic energy of the system is equal to

Answer 1

very interesting question !

A thin hollow sphere of mass m is completely filled with non - viscous liquid of mass m.

there are two components of kinetic energy of the system, rotational and translational.

rotational kinetic energy is only contributed by hollow sphere as liquid is non-viscous , liquid is presumably not rotating.

so, rotational kinetic energy of hollow sphere = 1/2 Iw²

we know, w is angular frequency i.e., w = v/r

and moment of inertia of hollow sphere about an axis passing through diameter of it , I = 2/3 mr²

so, rotational kinetic energy = 1/2 × 2/3 mv² = 1/3 mv² .....(1)

translational kinetic energy = kinetic energy of hollow sphere + kinetic energy of liquid

= 1/2 mv² + 1/2 mv²

= mv²

now, total kinetic energy = mv² + 1/3mv²

= 4/3 mv²

hence, answer is 4/3 mv²