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.

Question

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.

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.

Smart Achievers · Accepted Answer

(4)

$By conservation of energy, we have \frac{1}{2} m v_{c}^{2} + \frac{1}{2} I_{c} ω^{2} = m g h$

$Moment of inertia of solid and hollow cylinders are given as I_{solid} = \frac{M R^{2}}{2}, I_{hollow} = M R^{2}$

$For pure rolling, we have ω = \frac{v_{c}}{R}, As I_{solid} < I_{hollow} \Rightarrow v_{solid} > v_{hollow}$

$Hence solid cylinder will reach the bottom first.$

Solution

1 Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

2 Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

3 Statement-1 is True, Statement-2 is False

4 Statement-1 is False, Statement-2 is True

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