Question

A pendulum with bob of mass $m$ is oscillating on either side from its resting position $A$ between the extremes $B$ and $C$ at a vertical height $h$ above $A$. What is the kinetic energy $K$ and potential energy $U$ when the pendulum is at

• A. $K=0,U=0$
• B. $K=mgh/2,U=mgh/2$
• C. $K=mgh,U=0$
• D. $K=0,U=mgh$

Answer 1

The correct option is C $K=mgh,U=0$

When the pendulum is at position A it did not move from its equilibrium position hence it does not possess potential energy as it is defined by virtue of its state.Here it has maximum velocity by which it can be said that it has kinetic energy which is defined by virtue of its motion.Hence at point A it has only kinetic energy that $K=mgh,U=0$.Kinetic energy is written in terms of given quantities at point B and C total energy would be $mgh$ as energy is conserved it will have mgh even at point A.