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.
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.

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

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

Statement-1 is True, Statement-2 is False

Statement-1 is False; Statement-2 is True.

answer is D.

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Detailed Solution

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

Question Image

Moment of inertia of solid and hollow cylinders are given as
$I_{s o l i d} = \frac{M R^{2}}{2} I_{h o l l o w} = M R^{2}$
For pure rolling , we have
$ω = \frac{v_{c}}{R} A s I_{s o l i d} < I_{h o l l o w} \Rightarrow v_{s o l i d} > v_{h o l l o w}$
Hence solid cylinder will reach the bottom first.