question_answer

Length of a simple pendulum is \[I\]and its maximum angular displacement is \[\theta \] then its maximum K.E. is :

A) \[mgl\,\sin \,\theta \]                   

B)                        \[mgl(1+\,\sin \,\theta )\]           

C)                         \[mgl(1+\,\cos \,\theta )\]         

D)        \[mgl(1-\,\cos \,\theta )\]

Correct Answer: D

Solution :

\[h=l-I\cos \theta =l(1-\cos \theta )\] From law of conservation of momentum \[\frac{1}{2}m{{\upsilon }^{2}}=mgh=mgl\,(1-\cos \theta )\]