JEE Main20205 Sep 2020Morning ShiftPhysicsRotational MotionActual
A wheel is rotating freely with an angular speed ω 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 3 I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:
Options
- A5 6
- B1 4
- C0
- D3 4
Correct answer
D. 3 4
Step-by-step solution
From angular momentum conservation I ω + 0 = I ω C + 3 I ω C ω c = ω 4 Loss of kinetic energy = 1 2 I ω 2 - 1 2 ( I + 3 I ) ω 4 2 = 1 2 I ω 2 - 1 2 I ω 2 4 = 3 8 I ω 2 Fractional loss = 3 4