Question

Two rigid bodies $A$ and $B$ rotate with angular momenta $L_A$ and $L_B$ respectively. The moments of inertia of $A$ and $B$ about the axes of rotation are $I_A$ and $I_B$ respectively. If $I_A=I_B/4$ and $L_A=5L_B$. Then the ratio of rotational kinetic energy $K_A$ of $A$ to the rotational energy $K_B$ of $B$ is given by

• A. $\frac{K_A}{K_B}=\frac{25}{4}$
• B. $\frac{K_A}{K_B}=\frac{5}{4}$
• C. $\frac{K_A}{K_B}=\frac{1}{4}$
• D. $\frac{K_A}{K_B}=100$

Answer 1

The correct option is D $\frac{K_A}{K_B}=100$

Rotational K.E, $K=\frac{1}{2}I{w}^2$

Also, $L=Iw⟹K=\frac{L^2}{2I}$

$\frac{K_A}{K_B}=\frac{L_A^2}{L_B^2}\frac{I_B}{I_A}$

$\frac{K_A}{K_B}=\frac{25L_B^2}{L_B^2}\frac{4I_A}{I_A}$

$\frac{K_A}{K_B}=100$