Question

A simple pendulum of length $l$ has a maximum angular displacement $\theta$. The maximum kinetic energy of the bob is

• A. $ mgl (1-cos\theta ) $
• B. $1/2 \, mgl $
• C. $ mgl $
• D. $0.5\, mgl $

Answer 1

Answer: (A)

Here: length of pendulum $ =l $
Maximum angular displacement $ =\theta $
mass of the bob $ =m $
Now height of the bob at maximum angular displacement is
$ h=l-l\cos \theta =l(1-\cos \theta ) $
Also at the end of the displacement kinetic energy of the bob = potential energy of the bob
$ h=mgh=mgl\,(1-cos\theta ) $