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 becomes zero at the highest point.
(c) The kinetic energy of the ball in initial position was 1/2 mv2 =mgl
(d) The particle again passes through the initial position
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(a) The string becomes slack when the particle reaches its highest point.
(d) The particle again passes through the initial position
Explanation:
Since the particle is just able to complete the circle, at the highest point only its weight keeps it in circular path and tension in the string will be zero, Answer (a).
(b) is not true because as given the particle completes a circle. At the highest point, it must have horizontal velocity =√(gl).
(c) is not true because initial K.E. should be equal to ½mv² =mgl+½mgl.
(d)Since no further work is done on the particle by an external force, the total mechanical energy of the system remains constant and the particle passes the initial position with same initial velocity.
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