Question

The position of axis of rotation of a body is changed so that its moment of inertia decreases by 36%. The % change in its radius of gyration is

• A. Decreases by 18%
• B. Increases by 18%
• C. Decreases by 20%
• D. Increases by 20%

Answer 1

The correct option is C

Decreases by 20%

Moment of inertia decreases by 36 %.

So, if I is intial moment of inertia , 64% of I is the final moment of inertia .

$\therefore$ As I = M $K^2$.

I $\alpha$ $K^2$.

$\Rightarrow$ $\frac{I_2}{I_1}$ = $\frac{{K_2}^2}{{K_1}^2}$ $\Rightarrow$ $K_2$ = ( $\sqrt{\frac{I_2}{I_1}}$ $K_1$

$\Rightarrow$ $K_2$ = [ $\sqrt{\frac{\left(0.64\right)I}{I}}$] $K_1$ $\Rightarrow$ $K_2$ = 0.8 $K_1$

$\therefore$ %Change in radius of gyration = $\frac{(K_2-K_1)}{K_1}$ * 100

= - 20%

$\therefore$ Radius of gyration decreases by 20 %