In the figure shown, a bob attached with a light string of radius R is given an initial velocity u = 4 g R at the bottommost point. (a) At what height string will slack. (b) What is velocity of the

Question

In the figure shown, a bob attached with a light string of radius R is given an initial velocity u = 4 g R ​ at the bottommost point. (a) At what height string will slack. (b) What is velocity of the bob just before slacking of string.

TestHub · Accepted Answer

(a) The string slacks when T = 0 : R m v 2 ​ = m g sin θ . Energy: 2 1 ​ m u 2 = 2 1 ​ m v 2 + m g R ( 1 + sin θ ) , with u 2 = 4 g R , gives 2 g R = 2 g R s i n θ ​ + g R ( 1 + sin θ ) , so sin θ = 3 2 ​ . Height above the bottom: h 1 ​ = R ( 1 + sin θ ) = 3 5 ​ R . (b) v = u 2 − 2 g h 1 ​ ​ = 4 g R − 3 10 g R ​ ​ = 3 2 g R ​ ​ .

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