MHTCET 5 May 2025 Shift 2 Paper

Concept:Rotational kinetic energy and angular momentum both depend on moment of inertia and angular velocity, so changing frequency and energy alters the moment of inertia.Explanation:Let the initial moment of inertia be $I$ and angular velocity be $\omega$.The initial angular momentum is $L = I\omega$.Initial rotational kinetic energy is $K = \frac{1}{2} I\omega^{2}$.Since frequency is tripled, the new angular velocity is $\omega' = 3\omega$.The new kinetic energy is one-third of the initial value.So, $K' = \frac{K}{3} = \frac{1}{3}\left(\frac{1}{2} I\omega^{2}\right)$.Let the new moment of inertia be $I'$.Then, $K' = \frac{1}{2} I'(\omega')^{2} = \frac{1}{2} I'(3\omega)^{2} = \frac{9}{2} I'\omega^{2}$.Equating both expressions for $K'$:$\frac{9}{2} I'\omega^{2} = \frac{1}{6} I\omega^{2}$.Cancelling $\omega^{2}$ and simplifying gives $I' = \frac{I}{27}$.Now the new angular momentum is $L' = I'\omega' = \left(\frac{I}{27}\right)(3\omega) = \frac{I\omega}{9}$.Since $I\omega = L$, we get $L' = \frac{L}{9}$.Answer:$L' = \frac{1}{9}L$Correct option: A