Q. If a simple pendulum of length $l$ has maximum angular displacement $\theta$, then the maximum kinetic energy of bob of mass m is
A) $\frac{1}{2} \times \left( \frac{l}{g} \right)$
B) $\frac{1}{2} \times \frac{mg}{l}$
C) $mgl\ \times (1 - \cos\theta$)
D) $\frac{1}{2} \times mgl\sin\theta$
Explanation
(c) $AC = l\cos\theta$
$\therefore\ \ \ OC = OA - AC$
$= l - l\cos\theta = l(1 - \cos\theta)$
Max. KE of bob at $O =$Max. PE of bob at $B$
$= mg \times OC = mgl\ (1 - \cos\theta)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.