Discussion Forum



1)

A simple pendulum of length l has maximum angular  displacement  $\theta$ . The maximum kinetic energy of the bob of mass m is (g= acceleration  due to gravity)


A) $mgl(1+\cos \theta)$

B) $mgl(1+\cos ^{2} \theta)$

C) $mgl(1-\cos \theta)$

D) $mgl(\cos \theta-1)$

Answer:

Option C

Explanation:

According to question , when bob is at rest, the pendulum has only potential energy

 (PE)=mgl

When bob displaced by smaller  angular  displacement $\theta$ , the pendulum loses PE of bob and it gets converted into kinetic energy (KE).

So, from conservation of energy 

Loss in PE = gain in KE

$\therefore$     KE= mgl-mgl cos $\theta$ = $mgl(1-\cos \theta)$