Question

The angular momentum of two rotating bodies is equal. If the ratio of their moments of inertia is 1:4, the ratio of their rotational kinetic energies is:

• A. 1:2
• B. 2:1
• C. 1:4
• D. 4:1

Answer 1

The correct option is D 4:1

$RotationalkineticEnergy=\frac{L^2}{2I}$ (standard formula of energy in terms of angular momentum)

Directly putting the given data in formula and taking the ratio)
$\Rightarrow \frac{K.E_1}{K.E_2}=\frac{I_2}{I_1}=\frac{4}{1}$