Question

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. $m g l \times(1-\cos \theta)$
• D. $\frac{1}{2} \times m g l \sin \theta$

Answer 1

Answer: (C)

From the figure, $A C=l \cos \theta$

$\therefore O C=O A-A C$
$=l-l \cos \theta=l(1-\cos \theta)$
Maximum $KE$ of bob at $O=$ Maximum $PE$ of bob at $B$
$= ma \times O C=m g l(1-\cos \theta)$