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 -

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 -, 0 °, 30 °, 6 0 °, 90 °

MARKS App · Accepted Answer

∴ T m a x = m v A 2 l + m g ∴ 2 m g = m v A 2 l + m g ⇒ v A = g l ∴ v 2 = v A 2 - 2 g l 1 - cos ⁡ θ ∴ 0 = g l - 2 g l 1 - cos ⁡ θ ⇒ cos ⁡ θ = 1 / 2 ⇒ θ = 60 °

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