Question

Radius of gyration of a solid cylinder of radius $R$ and length $L$ about its long axis of symmetry is

• A. $R$
• B. $\frac{R}{\sqrt{2}}$
• C. $\sqrt{2} R$
• D. $\frac{R}{2}$
• E. $2 R$

Answer 1

Answer: (B)

If a body has mass $M$ and radius of gyration is $K$, then moment of inertia is, $I=M K^2$
or $K=\sqrt{\frac{l}{M}}$
For a solid cylinder about its long axis of symmetry,
$I=\frac{1}{2} M R^2$
Putting this value in above equation, we get
$ \Rightarrow K=\sqrt{\frac{\frac{1}{2} M R^2}{M}} $
$ \Rightarrow K=\frac{R}{\sqrt{2}}$