First slide

Rolling motion

Question

Two identical solid cylinders roll from rest on two identical inclined planes of slant lengths s and 2s but of the same height h. Then, the velocities, $v_{1}$ and $v_{2}$ acquired by the cylinders when they reach the bottom of the incline are related as

Moderate

A

$v_{1} = v_{2}$
B

$v_{1} = 2 v_{2}$
C

$2 v_{1} = v_{2}$
D

none of the above

Solution

For pure rolling , kinetic energy of a solid cylinder = $\frac{1}{2} m v^{2} + \frac{1}{2} (\frac{1}{2} m R^{2}) = \frac{3}{4} m v^{2}$
conserving energy , $\frac{3}{4} m v^{2} = m g h \Rightarrow v = \sqrt{\frac{4}{3} g h} t h e r e f o r e, v_{1} = v_{2}$

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