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  4. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

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Q. A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first ?

NEETNEET 2016System of Particles and Rotational Motion

Solution:

$a = \frac{g \sin\theta}{1+ \frac{K^{2}}{R^{2}}} $
for disc ; $ \frac{K^{2}}{R^{2}} = \frac{1}{2} = 0.5 $
for sphere ; $ \frac{K^{2}}{R^{2}} = \frac{2}{5} = 0.4 $
a(sphere) > a(disc)
$\therefore $ sphere reaches first