A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m s⁻¹ at t = 0 on a rough horizontal surface. It starts with purely sliding motion. After 2 s it acquires pure rolling. The total kinetic energy of the disc after 2 s will be ______ J. [Coefficient of friction = 0.3, g = 10 m s⁻²] Image
Physics · Circular Motion
JEE Mains 30 January 2023 Shift 2 Evening Shift

Question

A uniform disc of mass 0.5 kg and radius r is projected with velocity 18 m s⁻¹ at t = 0 on a rough horizontal surface. It starts with purely sliding motion. After 2 s it acquires pure rolling. The total kinetic energy of the disc after 2 s will be ______ J. [Coefficient of friction = 0.3, g = 10 m s⁻²] Image

Physics · Circular Motion

JEE Mains 30 January 2023 Shift 2 Evening Shift

G1 Physics · Accepted Answer

During sliding, translational acceleration a = −μg = −3 m s⁻². Hence after 2 s, v = 18−3×2 = 12 m s⁻¹. At pure rolling, ω = v/r. For a uniform disc, I = (1/2)mr². Total KE = (1/2)mv² + (1/2)Iω² = (1/2)mv² + (1/4)mv² = (3/4)mv² = (3/4)(0.5)(144)=54 J.