A bob attached to a light string of length R is given an initial velocity u = g R at the bottommost point of a vertical circle. (a) The string rotates through an angle θ from the downward vertical (

Question

A bob attached to a light string of length R is given an initial velocity u = g R ​ at the bottommost point of a vertical circle. (a) The string rotates through an angle θ from the downward vertical (the initial bottom position) when the velocity of the bob becomes zero. Find the value of θ . (b) If mass of the bob is m then what is the tension in the string when velocity becomes zero?

TestHub · Accepted Answer

(a) With u = g R ​ , the speed becomes zero when 2 1 ​ m u 2 = m g h : h ​ = 2 g u 2 ​ = 2 R ​ = R ( 1 − cos θ ) , ​ so cos θ = 2 1 ​ and θ = 6 0 ∘ . (b) At that point v = 0 , so the tension balances only the radial component of gravity: T = m g cos θ = 2 m g ​ .

Physics - Circular Motion Question with Solution | TestHub

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