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.
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.
- (A)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1
- (B)STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1
- (C)STATEMENT-1 is True, STATEMENT-2 is False
- (D)STATEMENT-1 is False, STATEMENT-2 is True✓ Correct
Answer: (D)
Solution
The acceleration of a rolling object down an incline is , where is the moment of inertia. A hollow cylinder has larger than a solid cylinder, so it has smaller acceleration and reaches the bottom later. STATEMENT-1 is false. By energy conservation, both have the same total kinetic energy at the bottom (equal to ), so STATEMENT-2 is true.
JEE Advanced · 2008 · 13 Apr 2008 · Paper 1 · Single correct option