Question

When a conservative force does positive work on a body,

• A. The potential energy increases
• B. The potential energy decreases
• C. Total energy increases
• D. Total energy decreases

Answer 1

The correct option is B

The potential energy decreases

The explanation for the correct option:

In case of option (B),

1. The conservative force produces a positive work on the body when it pushes or displaces the body towards the direction of the force.
2. As a result, the body draws closer to the source of force.
3. The distance between the body and the center of force decreases.
4. As a result, the body's potential energy is reduced but its kinetic energy is increased.
5. As a result, the potential energy of a body decreases when a conservative force does positive work on it.

Example:

In conservative force:

$$\begin{gathered} \overrightarrow{F}=\frac{-dV}{dr} \\ \overrightarrow{F}.\overrightarrow{dr}=-dV \end{gathered}$$

By integrating, we get

$\int \overrightarrow{F}.\overrightarrow{dr}=-\int dV$

When the work done is positive. $-dV$ is negative. So the potential energy decreases.

The explanation for the incorrect options (A), (C), and (D):

In the case of Option (A),

1. When a conservative force performs negative work on the body, the body's potential grows.
2. The kinetic energy decreases as the potential energy increases.

In the case of Option (C) and Option (D),

1. When a conservative force does positive work on a body, the body's potential and kinetic energy change.
2. As a result, maintain constant total energy.

Therefore, option B is the correct choice.