A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively k s p h : k c y l is 2 : x . The value of x is _______.

Question

Aicharya · Accepted Answer

Considering rotational axis as the diametrical axis for sphere and axis of cylinder. Then
$K_{1}^{2} = \frac{2}{5} R^{2}$ and $K_{2}^{2} = \frac{1}{2} R^{2}$
$∴ \frac{K_{1}}{K_{2}} = \sqrt{\frac{2 / 5}{1 / 2}} = \sqrt{\frac{4}{5}}$
$\Rightarrow \frac{K_{1}}{K_{2}} = \frac{2}{\sqrt{5}}$
Comparing it with the given value in the question,
$\frac{2}{\sqrt{5}} = \frac{2}{\sqrt{x}}$
$∴$ $x = 5$

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without…

Solution