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Oscillations
Question
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A simple pendulum of length l has a maximum angular displacement θ. The maximum kinetic energy of the bob is

  • mgl (1-cosθ)

  • 0.5 mgl

  • mgl

  • 0.5 mgl

Answer

A.

mgl (1-cosθ)

Here length of the pendulum = l

Maximum angular displacement =θ

Mass of the bob = m

Now height of the bob at maximum angular displacement is

h = l - l (1-cosθ)

Also at the end of displacement kinetic energy of the bob = potential energy of the bob

mgh = mgl (1-cosθ)

hence kinetic energy of the bob = mgl (1-cosθ)

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