Question

A ball is dropped on the ground from point A that is at the height $H$. After striking the ground, it rebounds and reaches back to point A, passing through point B that is at the height $h$, given $H>h$. Which of the following statement is correct?

Let $K.E{.}_A$ and $K.E{.}_B$ are the kinetic energies at A and B respectively. $P.E{.}_A$ and $P.E{.}_B$ are the potential energies at A and B respectively. Assuming the potential energy to be zero at the ground, choose the correct option.

• A. $K.E{.}_A>K.E{.}_B$, and $P.E{.}_A>P.E{.}_B$
• B. $K.E{.}_A<K.E{.}_B$, and $P.E{.}_A>P.E{.}_B$
• C. $K.E{.}_A>K.E{.}_B$, and $P.E{.}_A<P.E{.}_B$
• D. $K.E{.}_A<K.E{.}_B$, and $P.E{.}_A<P.E{.}_B$

Answer 1

The correct option is B $K.E{.}_A<K.E{.}_B$, and $P.E{.}_A>P.E{.}_B$

According to the law of conservation of energy, the sum of the potential energy
and the kinetic energy of the object would be constant.

Mathematically, $K.E{.}_A+P.E{.}_A=K.E{.}_B+P.E{.}_B$
Point A is above point B with respect to the ground. So, the potential energy of the ball at point A is greater than that of the ball at point B. Since, the sum of total energy needs to be constant, the kinetic energy of the ball at point A will be less than that of the ball at point B.
Therefore, option B is the correct answer.