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Conservation of mechanical energy

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 


As shown in Fig., the height attained by the bob when the string subtends an angle α with the vertical is


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 have



Hence the correct choice is (c).

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