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← IIT-JEE 2008 · Paper 1
PhysicsAssertion and reason+3 / -1Question 36 of 69

IIT-JEE 2008 · Paper 1, Physics question 36

STATEMENT-1: Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT-2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

Choose one option
Answer and worked solution

Official answer: D

Statement 2. Rolling without slipping wastes no energy, so each cylinder converts the same mghmgh into kinetic energy. True.

Statement 1. The hollow cylinder has the larger moment of inertia, so more of its energy goes into rotation: smaller speed and acceleration (a=gsin⁡θ1+I/mR2a=\frac{g\sin\theta}{1+I/mR^2}). The solid cylinder arrives first. False.

(D)