Question

The angular velocity of a body changes from one revolution per 9 second to 1 revolution per second without applying any torque. the ratio of its radius of gyration in the two cases is,

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

Answer 1

Answer: (D)

1 : 3

intial $I_i=m{r}_i^2$

$W_i=\frac{2\pi }{9}\frac{rad}{sec}$

final $I_f=m{r}_f^2$

$W_f=2\pi \frac{rad}{sec}$

$I_i{W}_i=I_f{W}_f$

$m{r}_i^2\times \frac{2\pi }{9}=m{r}_f^2\times 2\pi$

$(\frac{r_i}{r_f}{)}^2$ = 9

$\frac{r_i}{r_f}$ = 3