NTA Abhyas JEE Main2020PhysicsOscillationsPractice
A uniform rod of mass m and length L is hinged at one of its end with the ceiling and another end of the rod is attached with a thread which is attached with the horizontal ceiling at point P . If one end of the rod is slightly displaced horizontally and perpendicular to the rod and released. If the time period of small oscillation is 2 π 2 l sin θ x g . Find x .
Correct answer
3
Step-by-step solution
Consider a small angular displacement β Torque about the rotational axis τ = - m g l 2 sin θ β τ = I α 1 = m l sin θ 2 3 = m l 2 sin 2 θ 3 - m g l 2 sin θ β = m l sin 2 θ 3 α α = - 3 g 2 l sin θ β ∴ T = 2 π 2 l sin θ 3 g