Circular MotionHard

Question

A particle is moving in the vertical plane. It is attached at one end of a string of length l whose other end is fixed. The velocity at the lowest point is u. The tension in the string is and acceleration of the particle is at any position. Then, is zero at the highest point:   

Options

A.only if u ≤
B.if u =
C.only if u =
D.only if u >

Solution


= | T | | a | cosθ = 0
either  | T | = 0   or | a | = 0         or θ = 90o
a =   → for whole motion there is velocity.
So. T = 0
T = 0   for
T + mg =
T = − mg
mg 2l + mV2 = mu2
V2 u2 − 4gl
T = − 5mg
T = 0 or T < 0
u ≤       (B)

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