Question

A simple pendulum of length $l$ is performing S.H.M. with maximum angular displacement $\theta$. If the mass of the bob is $m$ then the maximum KE at its mean position is:

• A. $\frac{1}{2}m\left(\frac{l}{g}\right)$
• B. $\frac{mglsin\theta }{2}$
• C. $\frac{mgl}{2}$
• D. $mgl[1-cos\theta ]$

Answer 1

Answer: (D)

$mgl[1-cos\theta ]$

Applying conservation of energy, we get
$mgl=mglcos\theta +K.E$
$\therefore K.E=mgl(1-cos\theta )$