Question

A solid sphere is undergoing pure rolling. What is the ratio of its

translational kinetic energy to rotational kinetic energy?​

Answer 1

Moment of inertia of solid sphere about an axis passing through its centre is given by

I= 2/5 MR²

Velocity of centre of mass is given by v=Rω

Hence, translational kinetic energy is given by,

KEL = 1/2 MV ²

∴KEL= 1/2 MR²ω²

Rotational kinetic energy is given by

KER = 1/2 x 2/5 MR²ω²

Total kinetic energy,

KET = KEL + KER = 1/2 x 7/5 MR²ω²

Ratio of rotational kinetic energy to total kinetic energy is

KET/KER = 2/7