Question

A circular disc of mass m and radius r is rolling on a smooth horizontal surface with a constant speed v. Its kinetic energy is _____ 

(A) (1/4) mv² 

(B) (1/2) mv² 

(C) (3/4) mv² 

(D) mv²

Answer 1

Correct option: (C) (3/4) mv²

Explanation:

KE = (1/2)mv² + (1/2)Iω² --- both rotational and translation kinetic energies for disc, I = [(mR²) / 2]

KE =  (1/2)mv² + (1/2) ×[(mR²) / 2] × (v/R)² ----- v = rω

= (1/2)mv² + (1/4)mv² 

= (3/4)mv²