A simple pendulum of length l has a maximum angular displacement 8. The maximum kinetic energy of the bob is

Question

A simple pendulum of length l has a maximum angular displacement 8. The maximum kinetic energy of the bob is (A) mgl(1-cosθ) (B) 0.5mgl (C) mgl (D) 2 mgl

Tardigrade Admin · Accepted Answer

In SHM body is acted upon by a restoring force which tends to bring it in equilibrium position. Due to this force there is potential energy. Also as the body is moving it has kinetic energy.
During oscillation the two energies convert into each other.
Height of bob at maximum angular dispiacement is
h =lI - lcos

θ = l (l - cos θ)

Also,

PE = K E

m g h = m g l (1 - cos θ)

Q. A simple pendulum of length l has a maximum angular displacement 8. The maximum kinetic energy of the bob is

mgl(1-cos $θ$ )

0.5mgl

mgl

2 mgl