In motion of an object under the gravitational influence of another object. Which of the following quantities is not conserved ?

Options

A. Angular momentum
B. Mass of an object
C. Total mechanical energy
D. Linear momentum

Explanation

To determine which quantity is not conserved in the motion of an object under the gravitational influence of another object, we need to analyze the four options provided: angular momentum, mass, total mechanical energy, and linear momentum.

### Step-by-Step Solution:

1. **Understanding the Forces Involved**:
- When an object is under the gravitational influence of another object, it experiences a gravitational force. According to Newton's law of gravitation, the force \( F \) between two masses \( M \) and \( m \) separated by a distance \( x \) is given by:
\[ F = \frac{G \cdot M \cdot m}{x^2} \]
- Here, \( G \) is the gravitational constant.

2. **Analyzing Angular Momentum**:
- The gravitational force is a central force, meaning it acts along the line connecting the centers of the two masses. The torque \( \tau \) about the center of mass due to this force is zero because the line of action of the force passes through the center of mass.
- Since torque is zero, the angular momentum \( L \) of the system is conserved:
\[ \frac{dL}{dt} = 0 \implies L \text{ is constant} \]

3. **Analyzing Mass**:
- The mass of an object does not change due to gravitational influence. It is a fundamental property of matter and is conserved:
\[ \text{Mass is conserved} \]

4. **Analyzing Total Mechanical Energy**:
- In a system where only conservative forces (like gravity) are acting, the total mechanical energy (kinetic energy + potential energy) is conserved. Therefore:
\[ \text{Total mechanical energy is conserved} \]

5. **Analyzing Linear Momentum**:
- Linear momentum \( p \) is defined as:
\[ p = m \cdot v \]
- While the mass \( m \) remains constant, the velocity \( v \) of the object changes as it moves closer to the other mass due to the gravitational force acting on it. As a result, the linear momentum of the object changes:
\[ \text{Linear momentum is not conserved} \]

### Conclusion:
Based on the analysis, the quantity that is **not conserved** in the motion of an object under the gravitational influence of another object is **linear momentum**.

### Final Answer:
**Linear momentum is not conserved.**

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