Question

Two rotating bodies $A$ and $B$ of masses $m$ and $2m$ with momenta of inertia $I_A$ and $I_B(I_B>I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momenta respectively, then -

• A. $L_A=\frac{L_B}{2}$
• B. $L_A=2L_B$
• C. $L_B>L_A$
• D. $L_A>L_B$

Answer 1

Answer: (C)

$K.E_A=K.E_B$
$\frac{1}{2}{I}_A{\omega }_A^2=\frac{1}{2}{I}_B{\omega }_B^2$
$\frac{{\omega }_A}{{\omega }_B}=\sqrt{\frac{I_B}{I_A}}$ .....(i)
$L_A=I_A{\omega }_A{L}_B=I_B{\omega }_B$
$\frac{L_A}{L_B}=\frac{I_A}{I_B}\times \frac{{\omega }_A}{{\omega }_B}=\frac{I_A}{I_B}\times \sqrt{\frac{I_A}{I_B}}$
$=\sqrt{\frac{I_A}{I_B}}<1$
$\left[L_A<L_B\right]$