A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10⁻³ J. The speed of the centre of mass of the sphere is ______ cm s⁻¹.
Physics · Circular Motion
JEE Mains 31 January 2023 Shift 1 Morning Shift

Question

A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 × 10⁻³ J. The speed of the centre of mass of the sphere is ______ cm s⁻¹.

G1 Physics · Accepted Answer

For a rolling solid sphere, K = (1/2)Mv² + (1/2)(2/5 MR²)(v²/R²) = (7/10)Mv². Thus 7×10⁻³ = (7/10)(1)v², giving v² = 10⁻² and v = 0.1 m s⁻¹ = 10 cm s⁻¹.