Question

A simple pendulum of length l has maximum angular displacement θ. The maximum kinetic energy of the bob of mass m is ______.

(g = acceleration due to gravity)

Options

• mgl (1 + cosθ)

• mgl (1 + cos²θ)

• mgl (1 - cosθ)

• mgl (cosθ - 1)

Answer 1

A simple pendulum of length l has maximum angular displacement θ. The maximum kinetic energy of the bob of mass m is mgl (1 - cosθ).

(g = acceleration due to gravity)

Explanation:

Potential energy of pendulum, when bob is at rest, is given by

(PE) = mgl

The pendulum will lose the potential energy (PE) of the bob when it is moved by a small angular displacement θ, which is then transformed into kinetic energy (KE). therefore, based on energy conservation.

Loss in PE = gain in KE

∴ KE = mgl - mgl cosθ

= mgl (1 - cosθ)