Question

The rotational kinetic energy of two bodies of moments of inertia $9kg-m^2$ and $1kg-m^2$ are same. The ratio of their angular moments is

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

Answer 1

Answer: (A)

$3:1$

We have $\frac{1}{2}{I}_1{\omega }_1^2=\frac{1}{2}{I}_2{\omega }_2^2$

Thus $\frac{I_1}{I_2}=\frac{{\omega }_2^2}{{\omega }_1^2}$

or

$\frac{{\omega }_2}{{\omega }_1}=\frac{3}{1}$

$KE=\frac{L^2}{2I}$

Dince KE is same for both, $\frac{L_1^2}{2I_1}=\frac{L_2^2}{2I_2}$

$\Rightarrow \frac{L_1}{L_2}=\sqrt{\frac{I_1}{I_2}}=\sqrt{\frac{9}{1}}=3$