A bob of heavy mass m is suspended by a light string of length l . The bob is given a horizontal velocity v 0 as shown in figure. If the string gets slack at some point P making an angle θ from the

Question

A bob of heavy mass m is suspended by a light string of length l . The bob is given a horizontal velocity v 0 ​ as shown in figure. If the string gets slack at some point P making an angle θ from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v 0 ​ is : NEET 2025

TestHub · Accepted Answer

C.O.M.E. 2 1 ​ mv 0 2 ​ = mg ℓ ( 1 + sin θ ) + 2 1 ​ mv p 2 ​ .... ( 1 ) At pt P Tp + mg sin θ = ℓ mv p 2 ​ ​ ( as T p ​ = 0 ) mg sin θ = ℓ mv p 2 ​ ​ ⇒ mv p 2 ​ = mg ℓ sin θ …… . ( ii ) From (i) & (ii) ​ 2 1 ​ m v 0 2 ​ = m g ℓ ( 1 + sin θ ) + 2 1 ​ m g ℓ sin θ v 0 2 ​ = 2 g ℓ ( 1 + sin θ ) + g ℓ sin θ v 0 ​ = 2 g ℓ + 3 g ℓ sin θ ​ .... ( iii ) ​ ​ v p ​ = g ℓ sin θ ​ v 0 ​ = 2 g ℓ + 3 g ℓ sin θ ​ v 0 ​ v p ​ ​ = 2 + 3 sin θ sin θ ​ ​ ​

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