JEE Main20209 Jan 2020Evening ShiftPhysicsRotational MotionActual
A uniformly thick wheel with moment of inertia I and radius R is free to rotate about its centre of mass (see fig). A massless string is wrapped over its rim and two blocks of masses m 1 and m 2 m 1 > m 2 are attached to the ends of the string. The system Is released from rest. The angular speed of the wheel when m 1 descends by a distance h is:
Options
- A2 m 1 - m 2 g h m 1 + m 2 R 2 + I 1 2
- B2 m 1 + m 2 g h m 1 + m 2 R 2 + I 1 2
- Cm 1 - m 2 m 1 + m 2 R 2 + 1 1 2 g h
- Dm 1 + m 2 m 1 + m 2 R 2 + I 1 2 g h
Correct answer
A. 2 m 1 - m 2 g h m 1 + m 2 R 2 + I 1 2
Step-by-step solution
T E i   = T E f K i + U i = K l i n e a r + K r o t a t i o n a l + U f i n a l 0 + 0 = 1 2 m 2 v 2 + 1 2 m 1 v 2 + 1 2 I ω 2 - m 1 g h + m 2 g h 2 m 1 - m 2 g h m 1 + m 2 + I R 2 R 2 = ω 1 R 2 m 1 - m 2 g h m 1 + m 2 + I R 2