question_answer

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) \[0.5\,\,mgl\]

C) \[mgl\]                

D)        \[2\,\,mgl\]

Correct Answer: A

Solution :

In the equilibrium position energy is in the form of kinetic energy. Height of bob at maximum angular displacement is                 \[h=l-l\cos \theta \]                    \[=l(1-\cos \theta )\] Also   \[PE=KE\]          \[mgh=mgl(1-\cos \theta )\]