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A pendulum has a length l. Its bob is pulled aside from its equilibrium position through an angle α and then released. The speed of the bob when it passes through the equilibrium position is given by 

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a
2gl
b
2glcos⁡α
c
2gl(1−cos⁡α)
d
2gl(1−sin⁡α)

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detailed solution

Correct option is C

As shown in Fig., the height attained by the bob when the string subtends an angle α with the vertical ish=l−lcos⁡α=l(1−cos⁡α)Its potential energy at the highest point A = mgh, Where m is the mass of the bob. Let v be the speed of the bob when it passes through O. Its kinetic energy at O=12mv2. From the principle of conservation of energy, we have12mv2=mghv=2gh=2gl(1-cosα)Hence the correct choice is (c).

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