A particle of mass $m$ is attached to a light string of length $l$ , the other end of which is fixed. Initially the string is kept horizontal and then particle is given an upward velocity $v$ so that it is just able to complete the circle. Then:

the string becomes slack when the particle reaches the highest point.

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the velocity of the particle becomes zero at the highest point.

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the KE of the ball at highest position was

\frac{1}{2} m v^{2} = m g l

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the particle again passes through initial position

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Solution

The correct options are
A the string becomes slack when the particle reaches the highest point.
D the particle again passes through initial position
If the particle need to complete the whole circle.It should be just taut at top most point.and it would come to the starting point as no energy is lost in the path.
So, options A,D are correct.

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Q. A particle of mass m is attached to a light string of length l, the other end of which is fixed. Initially the string is kept horizontal and the particle is given an upward velocity v. The particle is just able to complete a circle.
(a) The string becomes slack when the particle reaches its highest point.
(b) The velocity of the particle become zero at the highest point.
(c) The kinetic energy of the ball in initial position was

\frac{1}{2} m v^{2} = m g l

(d) The particle again passes through the initial position.

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A particle of mass m is attached to a light string of length l, the other end of which is fixed. Initially the string is kept horizontal and then particle is given an upward velocity v so that it is just able to complete the circle. Then:

A particle of mass $m$ is attached to a light string of length $l$ , the other end of which is fixed. Initially the string is kept horizontal and then particle is given an upward velocity $v$ so that it is just able to complete the circle. Then: