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Question

A simple pendulum of string length l and bob of 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.


A

m(g+v2l)

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B

2mghl

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C

mg(1+hl)

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D

mg(1+2hl)

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Solution

The correct options are
A

m(g+v2l)


D

mg(1+2hl)


P.E. at point P = mgh. If friction is neglected, the potential is completely converted into kinetic energy when the bob reaches the equilibrium position O (see fig). If V is the velocity of the bob at O, then

12mV2=mgh

or V2=2gh

At position O, the tension F in the string is given by
F – mg = centripetal force

=mV21

or F=mg+mV21

=mg+2mghl

or F=mg(1+2hl)

Hence the correct choices are (a) and (d)


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