Question

The angular velocity of a body changes from one revolution per $9$ second to $1$ revolution per second. The ratio of its radius of gyration in the two cases is
(Assume that net torque applied is zero)

• A. $1:9$
• B. $3:1$
• C. $9:1$
• D. $1:3$

Answer 1

The correct option is B $3:1$

As net torque is zero,
Angular momentum is zero
$I_1{\omega }_1=I_2{\omega }_2$
$\Rightarrow m{r}_1^2\frac{2\pi }{9}=m{r}_2^2\frac{2\pi }{1}$
$\Rightarrow {\left(\frac{r_1}{r_2}\right)}^2=\frac{9}{1}$
$\Rightarrow \frac{r_1}{r_2}=\frac{3}{1}$