A body is falling freely under the action of gravity alone in vacuum. Which of the following quantities remain constant during the fall ?

Options

A. Kinetic energy.
B. Potential energy.
C. Total mechanical energy
D. Total linear momentum

Explanation

To solve the question regarding which quantities remain constant during the free fall of a body under the action of gravity alone in a vacuum, we will analyze each quantity step by step.

### Step-by-Step Solution:

1. **Understanding Free Fall**:
- A body in free fall is only influenced by the force of gravity. In a vacuum, there is no air resistance, meaning the only force acting on the body is gravitational force.

2. **Kinetic Energy**:
- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
- As the body falls, its velocity (v) increases due to the acceleration caused by gravity (g). Therefore, since the velocity is increasing, the kinetic energy will also increase.
- **Conclusion**: Kinetic energy does not remain constant.

3. **Potential Energy**:
- Potential energy (PE) in the context of gravitational force is given by:
\[ PE = mgh \]
- As the body falls, its height (h) above the ground decreases. Since the height is decreasing, the potential energy will also decrease.
- **Conclusion**: Potential energy does not remain constant.

4. **Total Mechanical Energy**:
- Total mechanical energy (TME) is the sum of kinetic and potential energy:
\[ TME = KE + PE \]
- In a system where only conservative forces (like gravity) are acting, the total mechanical energy remains constant. As the body falls, the increase in kinetic energy will exactly balance the decrease in potential energy, keeping the total mechanical energy constant.
- **Conclusion**: Total mechanical energy remains constant.

5. **Total Linear Momentum**:
- Linear momentum (p) is given by:
\[ p = mv \]
- As the body falls, its velocity increases due to the gravitational force, which means that the momentum will also increase. Since there is an external force acting (gravity), the momentum is not conserved.
- **Conclusion**: Total linear momentum does not remain constant.

### Final Answer:
The quantity that remains constant during the fall of a body under the action of gravity alone in a vacuum is **Total Mechanical Energy**.