A solid sphere and a disc of same mass and radius starts rolling down a rough in

Question

A solid sphere and a disc of same mass and radius starts rolling down a rough inclined plane, from the same height the ratio of the time taken in the two cases is

Options:

A . 15:14

B . √15:√14

C . 14:15

D . √14:√15

Answer: Option D
:
D
Time of descent

t = \frac{1}{sin θ} \sqrt{\frac{2 h}{g} (1 + \frac{k^{2}}{R^{2}})} ∴ R a t i o = \sqrt{\frac{{(1 + \frac{k^{2}}{R^{2}})}_{s p h e r e}}{{(1 + \frac{k^{2}}{R^{2}})}_{d i s c}}} = \sqrt{\frac{1 + \frac{2}{5}}{1 + \frac{1}{2}}} = \sqrt{\frac{7}{5} \times \frac{2}{3}} = \sqrt{\frac{14}{15}}

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