A solid sphere of mass M and radius R spins about an axis passing through its centre making 600 rpm. Its kinetic energy of rotation is

Options

A. `(2)/(5) pi^2 MR`
B. `(2)/(5) pi M^2 R^2`
C. `80 pi MR`
D. `80 pi^(2) MR^(2)`

Answer

D

Explanation

Kinetic energy of rotation , `K_(R) = (1)/(2) I omega^(2)`
Here , `I = (2)/(5) MR^(2) , omega = (600 xx 2pi)/(60) = 20 pi` rad/s
`therefore K_(R) = (1)/(2) xx (2)/(5) MR^(2) (20 pi)^(2) = 80 pi^(2) MR^(2)`