First slide
Conservation of mechanical energy
Question

A pendulum has a length l. Its bob is pulled aside from its equilibrium position through an angle α and then released. The speed of the bob when it passes through the equilibrium position is given by 

Moderate
Solution

As shown in Fig., the height attained by the bob when the string subtends an angle α with the vertical is

h=llcosα=l(1cosα)

Its potential energy at the highest point A = mgh, Where m is the mass of the bob. Let v be the speed of the bob when it passes through O. Its kinetic energy at O=12mv2. From the principle of conservation of energy, we have

12mv2=mgh

v=2gh=2gl(1-cosα)

Hence the correct choice is (c).

Get Instant Solutions
When in doubt download our app. Now available Google Play Store- Doubts App
Download Now
Doubts App