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A ball of mass M at one end of a string of length L rotates in a vertical circle just fast enough to prevent the string from going slack the speed of the ball at the bottom of the circle is

A ball of mass M at one end of a string of length L rotates in a vertical circle just fast enough to prevent the string from going slack the speed of the ball at the bottom of the circle is

Grade:11

1 Answers

Arun
25750 Points
6 years ago
I think the speed is not meant tp be constant; as the mass falls it loses potential energy and gains kinetic energy. 

At the top its speed is given by mv^2/L = mg .as you say. 
So its kinetic energy at the top is (1/2)mv^2 = mgL/2 

At the bottom it has dropped a distance 2L, so its potential energy has decreased 2mgL. Its kinetic energy has increased by 2mgL. 

Total kinetic energy at bottom = mgL/2 + 2mgL = 5mgL/2 

At the bottom (1/2)mv^2 = 5mgL/2 
v = sqrt (5gL)

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