question_answer

The maximum angular displacement of simple pendulum of length\[l\]is\[\theta .\] Its maximum kinetic energy will be

A)  \[mgl\text{ }sin\theta \]           

B)  \[mgl\text{ }(1+sin\theta )\])

C)  \[mgl(1+cos\theta )\]    

D)  \[mgl\text{ }(1-\cos \theta )\]

Correct Answer: D

Solution :

 \[h=l-l\cos \theta \] The energy of pendulum at point A will be completely potential energy at point B will be kinetic energy. \[\Rightarrow \] \[\frac{1}{2}m{{v}^{2}}=mgh\] \[\frac{1}{2}m{{v}^{2}}=mgl(1-\cos \theta )\]