First slide
Conservation of mechanical energy
Question

A ball weight 1.0 kg is tied to a string 15cm long. Initially the ball is held in position such that the string is horizontal. The ball is now released .A nail N is situated vertically below the support at a distance L. The minimum value of L such that the string will be wound round the nail is  

Moderate
Solution

Velocity of bob at C should be  5g(radius of circle)

here length of string =R, distance of nail below support =L , required minimum velocity to have vertical circle =5g(R-L)

velocity of ball at bottom most point of circle is 2gR

equating the above two equations
5g(RL)=2gR

squaring on both sides
5(R-L) = 2R
3R = 5L
L= 35  R

distance of nail below support is

L= 35× 15 = 9cm
 

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