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In a simple pendulum of length l the bob is pulled aside from its equilibrium position through an angle θ and then released. The bob passes through the equilibrium position with speed:

1. √2g(l + cosθ)
2. √2g sinθ
3. √2g l
4. √2g(l − cosθ)

Correct answer: √2g(l − cosθ)

Solution

The potential energy at the maximum displacement is converted into kinetic energy at the equilibrium position. Using energy conservation, the speed at the equilibrium position is given by v = √(2g(l - lcosθ)) = √2g(l - cosθ).

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