question_answer

A simple pendulum of length has a maximum angular displacement 0. The maximum kinetic energy of the bob of mass m will be :

A) \[mgl(1-\cos \theta )\] 

B) \[mgl\cos \theta \]

C) \[2mgl\]                              

D) \[mgl\]

Correct Answer: A

Solution :

When a body oscillates in simple harmonic motion, it is acted upon by a restoring force which tends to bring the body in equilibrium position. Due to this force there is potential energy in the body. Also, as the body is in motion it has kinetic energy. During oscillation of the body the two energies convert into each other, but their sum remains the same. Let \[l\] is length of pendulum,\[\theta \] is angular displacement and m is mass of bob. KE=PE \[=mgh=mg(l-l\text{ }\cos \theta )\] \[=mg(l-\cos \theta )\]