A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 M g , t

Question

A pendulum consisting of a small sphere of mass M suspended by an inextensible and massless string of length l is made to swing in a vertical plane. If the breaking strength of the string is 2 M g , then the maximum angular amplitude of the displacement from the vertical can be

TestHub · Accepted Answer

T m a x = m v 2 l + m g ⇒ 2 m g = m v 2 l + m g ⇒ v = g l … 1 Using energy conservation Δ K E = Δ P E ∵ 1 2 m v 2 = m g h ∴ h = v 2 2 g = l 2 … 2 ∵ cos ⁡ θ = l - h l = 1 2 ∴ θ = 60 °

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