question_answer

A 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)         \[5\,mgl\]

Correct Answer: A

Solution :

[a] From the figure, it is clear that loss of height = AB = OB \[-\] OA \[=\ell -\ell \cos \theta =\ell (1-\cos \theta )\] Now, loss of P.E. =mgh \[=mg\ell (1-\cos \theta )\] Gain of K.E.\[=\frac{1}{2}m{{v}^{2}}\] \[\frac{1}{2}m{{v}^{2}}=mg\ell (1-\cos \theta )\]