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

Question

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 .

TestHub · Accepted Answer

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

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