Which of the following statements about the gravitational constant is true ?

Options

A. It is a force
B. It has no fruit
C. It has same value in all systems of unit
D. It does not depend on the nature of the medium in which the bodies are kept

Explanation

To determine which statement about the gravitational constant is true, we can analyze the properties of the gravitational force and the gravitational constant itself.

### Step-by-Step Solution:

1. **Understanding the Gravitational Constant (G)**:
The gravitational constant, denoted as \( G \), is a fundamental physical constant used in the calculation of gravitational forces between two bodies. It has a value of approximately \( 6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2 \).

2. **Properties of Gravitational Force**:
- The gravitational force is an attractive force that acts between any two masses.
- It is described by Newton's law of universal gravitation:
\[ F = G \frac{m_1 m_2}{r^2} \]
where \( F \) is the gravitational force, \( m_1 \) and \( m_2 \) are the masses, and \( r \) is the distance between the centers of the two masses.

3. **Conservative Nature of Gravitational Force**:
- The work done by a gravitational force in moving an object along a closed path is zero. This indicates that gravitational force is conservative.
- In conservative forces, the work done depends only on the initial and final positions, not on the path taken.

4. **Independence from Medium**:
- The gravitational force does not depend on the nature of the medium in which the masses are located. It acts in a vacuum as well as in any medium.

5. **Evaluating the Statements**:
- Based on the properties discussed, we can evaluate the given statements about the gravitational constant.
- If one of the statements claims that the gravitational force is conservative and does not depend on the medium, then that statement is true.

### Conclusion:
The correct statement about the gravitational constant is that the gravitational force is conservative in nature and does not depend on the nature of the medium.

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