A particle of mass ' m ' connected to a string of length ' ℓ ' which is rotating in a vertical circle such that the ratio of the maximum to the minimum tension in the string is 2 :

Question

A particle of mass ' m ' connected to a string of length ' ℓ ' which is rotating in a vertical circle such that the ratio of the maximum to the minimum tension in the string is 2 : 1 then find out the speed of the particle at the bottom most point.

TestHub · Accepted Answer

2 1 ​ mv 1 2 ​ = mg 2 ℓ + 2 1 ​ mv 2 2 ​ ⇒ V 2 2 ​ = V 1 2 ​ − 4 g ℓ T max ​ = mg + ℓ m 1 ​ V 1 ​ 2 ​ ....(i) T m i n ​ + m g = ℓ mV 2 2 ​ ​ ⇒ T m i n ​ = ℓ mV 2 2 ​ ​ − m g .....(ii) 2 = V 2 2 ​ − g ℓ V 1 2 ​ + g ℓ ​ ⇒ 2 V 2 2 ​ − 2 g ℓ = V 1 2 ​ + g ℓ 2 ( V 1 2 ​ − 4 g ℓ ) − 2 g ℓ = V 1 2 ​ + g ℓ 2 V 1 2 ​ − 8 g ℓ − 2 g ℓ = v 1 2 ​ + g ℓ ⇒ V 1 ​ = 11 g ℓ ​

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