A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ m s⁻¹.
Physics · Circular Motion
JEE Mains 29 January 2023 Shift 1 Morning Shift

Question

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere will be ____ m s⁻¹.

G1 Physics · Accepted Answer

For a solid sphere, I = (2/5)MR² and ω = v/R. Total kinetic energy = (1/2)Mv² + (1/2)Iω² = (1/2)Mv² + (1/5)Mv² = (7/10)Mv². With M = 2 kg, 2240 = (7/5)v², so v² = 1600 and v = 40 m s⁻¹.