A solid sphere and a solid cylinder of same mass and radius are r… - Vidyadip

Question

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 $\left( k _{\text {sph }}: k _{ cyl }\right)$ is $2: \sqrt{ x }$, then value of $x$ is .............

✓

Answer

For solid sphere $\frac{2}{5} mR ^2= mk _{ mph }^2$

$k _{ sph }=\sqrt{\frac{2}{5}} R$

For solid cylinder $\frac{ mR ^2}{2}= mk _{ cyl }^2$

$\Rightarrow k _{ cyl }=\frac{ R }{\sqrt{2}}$

$\frac{ k _{ rph }}{ k _{ cyl }}=\frac{\sqrt{\frac{2}{5}}}{\frac{1}{\sqrt{2}}}=\frac{2}{\sqrt{5}}=\frac{2}{\sqrt{ x }}$

$\therefore x =5$

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