First slide

Rolling motion

Question

A solid sphere and a disc of same radii are rolling down an inclined plane without slip. One reaches earlier than the other due to

Moderate

A

different radius of gyration
B

different size
C

different friction
D

different moment of inertia

Solution

THE TIME TAKEN TO ROLL DOWN IS GIVEN BY $T = \sqrt{\frac{2 L}{a}}$
$a = \frac{g \sin θ}{1 + \frac{I}{{MR}^{2}}} = \frac{g \sin θ}{1 + \frac{K^{2^{}}}{R^{2}}} [I = {MK}^{2}]$
Clearly one reaches earlier than other due to different radius of gyration.

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