Question

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

• A. 1 :2
• B. $\sqrt{2}:1$
• C. 2:1
• D. 1:$\sqrt{2}$

Answer 1

Answer: (D)

Rotational kinetic energy remains same
$i,e;\frac{1}{2}{I}_1{\omega }_1^2=\frac{1}{2}{I}_2{\omega }_2^2$
or $\frac{1}{2I_1}(I_1{\omega }_1{)}^2=\frac{1}{2I_2}(I_2\omega {)}^2$
or$\frac{L_1^2}{I_1}=\frac{L_2^2}{I_2}$
or $\frac{L_1}{L_2}=\sqrt{\frac{I_1}{I_2}}$
but $I_1=I,I_2=2I$
=$\frac{L_1}{L_2}=\sqrt{\frac{I}{2I}}=\frac{1}{\sqrt{2}},$
or $L_1:L_2=1:\sqrt{2}$