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A light string ABCDE whose midpoint is C passes through smooth rings B and D, which are fixed in a horizontal plane distant 2a apart. To each of the points A,C,E is attached a mass m. Initially C is held at rest at O(midpoint BD) and is then set free. What is the distance OC when C comes to instantaneous rest.

A light string ABCDE whose midpoint is C passes through smooth rings B and D, which are fixed in a horizontal plane distant 2a apart. To each of the points A,C,E is attached a mass m. Initially C is held at rest at O(midpoint BD) and is then set free. What is the distance OC when C comes to instantaneous rest.

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1 Answers

Chetan Mandayam Nayakar
312 Points
12 years ago

let answer be 'h'. BC=DC=√(a^2 +h^2)-a, therefore masses at A and E rise by this amount. from conservation of energy,

2mg(√(a^2 +h^2)-a)=mgh,upon solving this equation we get h=4a/3

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