question_answer

    A simple pendulum of length I has a maximum angular displacement 6. The maximum kinetic energy of the bob is

A)  \[mgl\text{ }(1-cos\text{ }\theta \text{)}\]        

B)  \[0.5\text{ }mgl\]

C)  \[mgl\]              

D)  \[0.5\text{ }mgl\]

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 \[=mgh=mgl(1-cos\theta )\]