Question

The value of quantity $G$ in the law of gravitation

• A. depends on mass of earth only
• B. depends on radius of earth only
• C. depends on both mass and radius of earth
• D. is independent of mass and radius of earth

Answer 1

The correct option is D

is independent of mass and radius of earth

The concept used- Universal law of gravitation

• According to the universal law of gravitation,

$F\propto \frac{m_1{m}_2}{r^2}$

On removing the sign of proportionality we get a constant of proportionality$G$, which is also called a universal gravitation constant having a constant value of$6.673\times {10}^{-11}{\mathrm{Nm}}^2{\mathrm{kg}}^{-2}$.

$F=\frac{G{m}_1{m}_2}{r^2}$

• From here we get the value of $G$, the universal constant of proportionality-

$G=\frac{F{r}^2}{m_1{m}_2}$

• As it is the force of attraction between two unit masses separated by unit distance and it is independent of mass and radius of the earth. so all options other than option (d) are incorrect. hence the value of $G$ is independent of the mass and radius of the earth.
• Hence the correct answer is an option (D).