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 -

• A. $\sqrt{2gh}$
• B. $\sqrt{\frac{3}{4}gh}$
• C. $\sqrt{\frac{4}{3}gh}$
• D. $\sqrt{4gh}$

Answer 1

Answer: (C)

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

Answer 2

$mgh = \frac{1}{2} mv ^{2}\left(1+ K ^{2} / R ^{2}\right)$
$\Rightarrow v =\sqrt{\frac{2 gh }{\left(1+ K ^{2} / R ^{2}\right)}}$