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A particle is rotated in a vertical circle by connecting it to a string of length l and keeping the other end of the string fixed. The minimum speed of the particle when the string is horizontal for which the particle will complete the circle is 

(a) √gl  (b) √2gl (c) √3gl (d) √5gl

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1 Answers

(c) √(3gl).

Explanation:- 

Let speed at the top = v, it is balanced by weight mg, so, mv²/l=mg 

→v²= gl 

Now let the speed when string is horizontal = v' 

Here total energy = ½mv'²=½mv²+mgl 

v'²=v²+2gl = gl+2gl =3gl 

v'= √(3gl)

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