First slide

Rolling motion

Question

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

Moderate

A

$\sqrt{(2 gh)}$
B

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

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

$\sqrt{(\frac{4 g}{h})}$

Solution

$\frac{1}{2} {Iω}^{2} + \frac{1}{2} {mv}^{2} = mgh, ω = \frac{v}{r}, I = \frac{1}{2} {mr}^{2}$
Solve to get v = $\sqrt{(\frac{4}{3}) gh}$

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