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Question: The ratio of the time taken by a solid sphere and that taken by a disc of the same mass and radius t...

The ratio of the time taken by a solid sphere and that taken by a disc of the same mass and radius to roll down a smooth inclined plane from rest from the same height –

A

15 : 14

B

15\sqrt{15} : 14\sqrt{14}

C

14 : 15

D

14\sqrt{14}: 15\sqrt{15}

Answer

14\sqrt{14}: 15\sqrt{15}

Explanation

Solution

t = 2sgsin⁡θ(1+K2R2)\sqrt{\frac{2s}{g\sin\theta}\left( 1 + \frac{K^{2}}{R^{2}} \right)}

t1t2\frac{t_{1}}{t_{2}}= 1+251+12\sqrt{\frac{1 + \frac{2}{5}}{1 + \frac{1}{2}}} = 1415\sqrt{\frac{14}{15}}