Question

A simple pendulum of length $l$ has maximum angular displacement $\theta .$ Then maximum kinetic energy of a bob of mass $m$ is

• A. $\frac{1}{2}mgl$
• B. $\frac{1}{2}mgl\cos \theta$
• C. $mgl(1-\cos \theta )$
• D. $\frac{1}{2}mgl\sin \theta$

Answer 1

The correct option is C $mgl(1-\cos \theta )$

At point B, $v=0$ and $P.E$ is maximum.

At point A, $P.E=0$ and $K.E$ is maximum.

Height of bob at B, $AP=l-lcos\theta =l(1-cos\theta )$

Thus $P.E=mgl(1-cos\theta )$

Applying conservation of energy at A and B, $K.E_m+0=0+P.E$

$⟹K.E_m=mgl(1-cos\theta )$