MHT CET20249 May 2024Morning ShiftPhysicsRotational MotionActual
A thin uniform rod of length ' L ' and mass ' M ', is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' '. Its centre of mass rises to a maximum height of [g= gravitational acceleration]
Options
- A^2 ~L ^2 12 ~g ^2
- B^2 L^2 g 6
- C^2 g 12 ~L ^2
- D^2 ~L ^2 24 ~g
Correct answer
D. ^2 ~L ^2 24 ~g
Step-by-step solution
The moment of inertia of rod about its centre is ML ^2 12 . Its kinetic energy K.E. = 1 2 I ^2= 1 2 ML ^2 12 ^2= M L^2 ^2 24 If its centre of mass rises by h, then it will gain potential energy. Potential energy, Mgh = ML ^2 ^2 24 h = L ^2 ^2 24 ~g .