What will be the formula of mass of the earth in terms of g, R and G ?

Question

What will be the formula of mass of the earth in terms of g, R and G ? (A) G (R/g) (B) g (R2/G) (C) g2(R/g) (D) G (g/R)

Tardigrade Admin · Accepted Answer

The gravitational force (F)=(G M m/R2) and F=m g. Equating both the values of gravitational force, (G M m/R2)=m g or M=g (R2/G), where M is the mass of the earth.

Q. What will be the formula of mass of the earth in terms of $g, R$ and $G$ ?

$G \frac{R}{g}$

$g \frac{R ^{2}}{G}$

$g^{2} \frac{R}{g}$

$G \frac{g}{R}$

The gravitational force $(F) = \frac{GM m}{R ^{2}}$ and $F = m g$ .
Equating both the values of gravitational force, $\frac{GM m}{R ^{2}} = m g$
or $M = g \frac{R ^{2}}{G}$ ,
where $M$ is the mass of the earth.

Q. What will be the formula of mass of the earth in terms of g,R and G ?

GgR​

gGR2​

g2gR​

GRg​