Question

the gravitational force between two point masses $m_1$ and $m_2$ at separation, r is given by

$F=k\frac{m_1{m}_2}{r^2}$
The constant k:
1. Depends on the system of units only

2. Depends on the medium between masses only
3. Depends on both (1) and(2)
4. Is independent of both (1) and (2)

Answer 1

1. The gravitational force between two point masses $m_{1}and{m}_2$ separated by a distance r is given by; $F=k\frac{m_1{m}_2}{r^2}$ .

2. The constant k is the proportionality constant which is replaced by G; the universal gravitational constant.

3. Thus, $k$ is a constant that does not vary with the medium in which the masses are placed.

4. The unit of the constant $k$ is $\frac{N{m}^2}{k{g}^2}$ , which will be different in CGS system as the unit of force in CGS system is dyne, the unit of mass in CGS system is gram(g) and the CGS unit of distance is centimetre(cm).

5. Due to the variation in the value of units in different systems of units for the physical quantity, the value of k varies.

6. The unit of k in the CGS system will be $\frac{dynec{m}^2}{g^2}$.

Thus,

Option 1) Depends on the system of units only is the correct option.