Q 11-06-199JEE MainJEE Main 2020 (5 Sep, Shift 1)Medium
A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is $I$ and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia $3I$ initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:
Answer: (D) $\dfrac34$
Angular momentum: $I\omega = 4I\omega' \Rightarrow \omega' = \dfrac\omega4$.
$$\frac{K_f}{K_i} = \frac{\tfrac12(4I)(\omega/4)^{2}}{\tfrac12I\omega^{2}} = \frac14$$
Fractional loss $= \dfrac34$.
Solution by Sreeraj P, M.Sc Physics