Question

A ball is thrown straight up. Neglecting air resistance, which statement is not true regarding the energy of the ball?

1. The potential energy decreases while the ball is going up.
2. The kinetic energy decreases while the ball is going up.
3. The sum of the kinetic energy and potential energy is constant.
4. The potential energy decreases when the ball is coming down.
5. The kinetic energy increases when the ball is coming down.

Short answer

Option (a):The potential energy decreases while the ball is going up.

Step-by-step solution

Definition of kinetic energy

The energy possessed by an object by virtue of its motion is known as kinetic energy.It is given by the formula:

\(KE = \frac{1}{2}m{v^2}\)

Definition of potential energy

The energy stored in an object by virtue of its position above the surface of the earth is known as potential energy.It is given by the formula:

\(PE = mgh\)

Here, g is the acceleration due to gravity and has a value of \(9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\).

Analysis of the energy of the ball

Initially (near the ground), the kinetic energy of the ball is the maximum, and its potential energy is zero. When it is thrown straight up, the kinetic energy starts gradually decreasing while rising. After some time, during its fall, the potential energy decreases because the ball's height from the ground decreases. This potential energy starts to convert into kinetic energy, which increases on returning to the ground.

Thus, option (a) is incorrect.