When a uniform solid sphere and a disc of the same mass and of the same radius rolls down an inclined smooth plane from rest to the same distance, then the ratio of the time taken by them is

Question

Dr. Abubacker · Accepted Answer

(c) $t = \frac{1}{\sin	heta}\sqrt{\frac{2h}{g}\left( 1 + \frac{K^{2}}{R^{2}} ight)}$
$\Rightarrow \frac{t_{S}}{t_{D}} = \sqrt{\frac{1 + \left( \frac{K^{2}}{R^{2}} ight)_{S}}{1 + \left( \frac{K^{2}}{R^{2}} ight)_{D}}}$
$= \sqrt{\frac{1 + \frac{2}{5}}{1 + \frac{1}{2}}} = \sqrt{\frac{14}{15}}$

Q. When a uniform solid sphere and a disc of the same mass and of the same radius rolls down an inclined smooth plane from rest to the same distance, then the ratio of the time taken by them is

Explanation

Reviewed by Dr. Abubacker

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