Question

The universal constant of gravitation(G) has the unit:

• A. N
• B. $m/s$
• C. $N{m}^2/k{g}^2$
• D. J

Answer 1

The correct option is C

$N{m}^2/k{g}^2$

The explanation for the correct option:

C: $N{m}^2/k{g}^2$

1. According to the formula of the gravitational force of attraction, $F=G\frac{Mm}{r^2}$.
2. So, $G=\frac{F{r}^2}{Mm}........\left(a\right)$
3. The unit of force is newton $\left(N\right)$, the unit of distance $r$ is meter $\left(m\right)$ and the unit of mass is $\left(Kg\right)$, on putting these values in equation (a), we get

$G=\frac{N{m}^2}{{Kg}^2}$

4. So, the unit of $G=N{m}^2/k{g}^2$.

The explanation for the incorrect option(s):

A: $N$

Newton $\left(N\right)$ is the unit of force.

B: $m/s$

$m/s$ is the unit of speed or velocity.

D: $J$

Joule $\left(J\right)$ is the unit of work or energy.

Hence, option C is correct.