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Q.

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

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a

15 cm

b

4 cm

c

9 cm

d

none of these

answer is C.

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Detailed 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 2gRequating the above two equations5g(R−L)=2gRsquaring on both sides5(R-L) = 2R3R = 5LL= 35  Rdistance of nail below support isL= 35× 15 = 9cm
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