The correct option is (c).
Explanation
According to Newton's Law of Universal Gravitation, every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This relationship is expressed mathematically as:
$F = G \frac{m_1 m_2}{r^2}$
Here, $F$ is the gravitational force, $m_1$ and $m_2$ are the masses, $r$ is the distance between them, and $G$ is the Universal Gravitation Constant.
Statement-wise Analysis:
- Statement 1 is Correct: The Universal Gravitation Constant ($G$) is a fundamental physical constant. Its value is intrinsic and universal, meaning it does not depend on the nature, size, or masses of the interacting bodies. It remains constant regardless of the properties of the objects involved.
- Statement 2 is Incorrect: The value of $G$ is invariant and does not change with the distance between the bodies. While the gravitational force ($F$) changes with distance (inverse square law), the proportionality constant ($G$) remains the same everywhere in the universe. It is also independent of the medium between the two bodies.
- Statement 3 is Correct: The SI unit of $G$ can be derived from the gravitation formula:
$G = \frac{F \times r^2}{m_1 \times m_2}$
Substituting the SI units for Force (Newton, $N$), distance (meter, $m$), and mass (kilogram, $kg$), the unit is:
$\frac{N \cdot m^2}{kg \cdot kg} = N m^2 kg^{-2}$
Key Takeaway:
The Universal Gravitation Constant ($G$) must not be confused with the acceleration due to gravity ($g$). While $g$ varies from place to place (depending on altitude, depth, and latitude), $G$ is a scalar universal constant with a fixed value of approximately $6.674 \times 10^{-11} N m^2 kg^{-2}$.