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 momentum will be in the ratio:

• A. 1:4
• B. $\sqrt 2$ :1
• C. 4:1
• D. 1:$\sqrt 2$

Answer 1

Answer: (D)

1:$\sqrt 2$

Answer 2

KE= $\frac{1}{2}$I $\omega$2 = $\frac{1}{2}\, \frac{L^2}{I}$

KE1 = KE2

$\frac{1}{2}\, \frac{L^2}{I_1}$ = $\frac{1}{2}\, \frac{L^2}{I_2}$

$\frac{L^2}{1}$=$\frac{L^2_2}{2}$

$\frac{L_1}{L_2}$ =$\frac{1}{\sqrt 2}$

1:$\sqrt 2$​

Therefore, the correct option is (D): 1:$\sqrt 2$​