A thin pole of length 1m is made to stand vertically on ground. One end of a massless thread of length 0.6 m is attached to top end of pole while at the other end a bob of mass 0.5 kg is fixed. Bob is

Question

A thin pole of length 1m is made to stand vertically on ground. One end of a massless thread of length 0.6 m is attached to top end of pole while at the other end a bob of mass 0.5 kg is fixed. Bob is released from rest from a position where string is taut and horizontal. An external torque τ ext ​ is needed about lower end of pole to keep it upright. Maximum value of τ ext ​ (in Nm ) will be ________.

TestHub · Accepted Answer

Energy conservation for the bob ( θ = angle of the thread from the pole): v 2 = 2 g ℓ cos θ . Centripetal equation: T = m g cos θ + ℓ m v 2 ​ = 3 m g cos θ . Torque about the lower end of the pole: τ = T h sin θ = 3 m g h sin θ cos θ = 2 3 ​ m g h sin 2 θ , maximum at θ = 4 5 ∘ : τ ma x ​ = 2 3 m g h ​ = 2 3 × 0.5 × 10 × 1 ​ = 7.50 N m

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