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  

Velocity of bob at C should be  $\sqrt{5g(radius of circle)}$

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

velocity of ball at bottom most point of circle is $\sqrt{2gR}$

equating the above two equations
$\sqrt{5g(R-L)=}\sqrt{2gR}$

squaring on both sides
5(R-L) = 2R
3R = 5L
L= $\frac{3}{5}$  R

distance of nail below support is

L= $\frac{3}{5}\times$ 15 = 9cm