question_answer

A simple pendulum of length \[I\] has a maximum angular displacement \[\theta \] The maximum kinetic energy of the bob is:

A)  \[mgl(1-\cos \,\theta )\]                             

B) \[0.5\,mgl\]                       

C)  \[mgl\]               

D)        \[0.5\,mgl\]

Correct Answer: A

Solution :

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