First slide

Rolling motion

Question

A solid sphere rolls down two different inclined planes of the same height but of different inclinations:

Moderate

A

the speeds will be same but time of descent will be different
B

in both cases, the speeds and time of descent will be same
C

speeds and time of descent both will be different
D

the speeds will be different but time of descent will be same

Solution

$As v = \sqrt{\frac{2 g h}{1 + \frac{I}{M R^{2}}}}$
Hence velocity is independent of the inclination of the plane and depends only on height h through which body descends. But because $t = \frac{1}{\sin θ} \sqrt{\frac{2 h}{g} (1 + \frac{I}{M R^{2}})}$ depends on the inclination also, hence greater the inclination lesser will be the time of descend. Hence, in present case, the speeds will be same (because h is same) but time is descend will be different (because of different inclinations)

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