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A pendulum consisting of a bob of mass 'm' and string of length l is moved upto the horizontal position A and released (see Figure). What should the minimum strength of the string be to withstand the tension as the pendulum passes through the position of equilibrium?

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When the bob is released from the horizontal position A, it will reach the equilibrium position O by moving along a circular path as shown in fig. above.

At the point O, the bob of the pendulum is acted upon by two, forces: its weight 'mg' and tension T in the string. The resultant of these forces provide the necessary centripetal force i.e.,

mv2/l = T - mg or, T = mv2/l + mg    ...(i)

The velocity 'v' can be determined by applying the principle of conservation of energy, i.e.,

Kinetic energy of the bob at the point O

= Potential energy at the point A

⇒ 1/2 mv2 = mgl ⇒ v = √{2gl}

In the equation (i), substituting for v, we have

T = {m(√{2gl})2}/{l} + mg = 3 mg

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