First slide

Rolling motion

Question

A solid cylinder of mass M and radius R rolls without slipping down an inclined plane of length L and height h. What is the speed of its centre of mass when the cylinder reaches its bottom ?

Moderate

A

$\sqrt{2 gh}$
B

$\sqrt{\frac{3}{4} gh}$
C

$\sqrt{\frac{4}{3} gh}$
D

$\sqrt{4 gh}$

Solution

$From COME, mgh = \frac{1}{2} {mv}^{2} (1 + \frac{K^{2}}{R^{2}}) \Rightarrow v = \sqrt{\frac{2 gh}{1 + \frac{K^{2}}{R^{2}}}}$

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