A simple pendulum of length / and bob mass m is displaced from its equilibrium position O to a position P so that the height of P above O is h, It is then released. What is the tension in the string when the bob passes through the equilibrium position O ? Neglect friction, v is the velocity of the bob at O.
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a
mgh/l
b
2mgh/l
c
mg(1+h/l)
d
mg(1+2h/l)
answer is D.
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Detailed Solution
The velocity v at equilibrium position O when released from position P is given by12mv2=mgh or v2=2gh At O, let the tension in the string be T. Then T−mg=mv2/l T=mg+mv2/l =mg+2mghl =mg1+2hl