A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If it rolls without slipping, its speed at the bottom is ______ m s⁻¹. [g = 10 m s⁻²] Image
Physics · Circular Motion
JEE Mains 1 February 2023 Shift 1 Morning Shift

Question

A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If it rolls without slipping, its speed at the bottom is ______ m s⁻¹. [g = 10 m s⁻²] Image

Physics · Circular Motion

JEE Mains 1 February 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Vertical drop h = 0.60 sin30° = 0.30 m. For a solid cylinder, I = (1/2)MR². Energy conservation gives Mgh = (1/2)Mv² + (1/2)I(v²/R²) = (3/4)Mv². Thus v² = 4gh/3 = 4, so v=2 m s⁻¹.