A closed circular tube of average radius 15 cm with rough inner walls is kept vertical. A 1 kg block just fits inside the tube and is introduced at the top with speed 22 m s⁻¹. After completing five oscillations, it stops at the bottom. The numerical answer reported by the source for work done by the tube on the block is ______ J. [g = 10 m s⁻²] Image
Physics · Circular Motion
JEE Mains 10 April 2023 Shift 1 Morning Shift

Question

A closed circular tube of average radius 15 cm with rough inner walls is kept vertical. A 1 kg block just fits inside the tube and is introduced at the top with speed 22 m s⁻¹. After completing five oscillations, it stops at the bottom. The numerical answer reported by the source for work done by the tube on the block is ______ J. [g = 10 m s⁻²] Image

Physics · Circular Motion

JEE Mains 10 April 2023 Shift 1 Morning Shift

G1 Physics · Accepted Answer

Initial kinetic energy: K(i) = (1/2)mv² = (1/2)(1)(22²) = 242 J The block finally stops at the bottom, which is 2R = 0.30 m below the starting point. Work done by gravity: W(g) = mg(2R) = 1×10×0.30 = 3 J Using the work-energy theorem: W(tube) + W(g) = K(f) − K(i) W(tube) + 3 = 0 − 242 Therefore, W(tube) = −245 J So the physical work done by the tube is −245 J. The source/NTA numerical key reports the magnitude 245. Final source-key value: 245