Question

In the relation $F=G\frac{Mm}{d^2}$, the quantity $G$

• A. depends on the value of $g$ at the place of observation
• B. is used only when the earth is one of the two masses
• C. is greatest at the surface of the earth
• D. is a universal constant of nature

Answer 1

The correct option is D

is a universal constant of nature

The explanation for Correct Option:

Option (D):

1. Newton's law of gravitation states that the gravitational force between two bodies is directly proportional to the product of the mass of the two bodies $\left(F\propto Mm\right)$.
2. Newton's law of gravitation states that the gravitational force between two bodies is inversely proportional to the square of the distance between the two bodies $\left(F\propto \frac{1}{d^2}\right)$.
3. Therefore, the total gravitational force can be expressed as $F=G\frac{Mm}{d^2}$, where $G$ is the universal gravitational constant.
4. The value of $G$ is $6.6\times {10}^{-11}N{m}^{2}k{g}^{-2}$.
5. Hence, a constant is always universal in nature and does not change anywhere.

The explanation for Incorrect Option:

Option (A):

1. $g$ is the value of acceleration due to gravity at a given point.
2. This can be derived from the gravitational constant $G$.
3. Hence, the quantity $G$ does not depend on the value of $g$ at the place of observation.

Option (B):

1. Since $G$ is the universal gravitational constant, its value is the same everywhere in the universe.
2. Therefore, the two masses can be of any two objects in the universe.
3. Hence, $G$ is not only used when the earth is one of the two masses.

Option (C):

1. Since $G$ is the universal gravitational constant, its value is the same everywhere in the universe.
2. The value $G$ does not depend on the position.
3. Hence, $G$ is same every where.

Hence, option D is correct.