question_answer

A simple pendulum of length \[l\] has a maximum angular displacement \[\text{ }\!\!\theta\!\!\text{ }\]. 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 \[h=l-l\cos \theta =l(1-\cos \theta )\] Also at the end of the displacement kinetic energy of the bob = potential energy of the bob \[h=mgh=mgl\text{ }(1-cos\theta )\]