Question

What will be the formula of mass of the earth in terms of acceleration due to gravity $\left(g\right),$ radius of earth $\left(R\right),$ and universal gravitation constant $\left(G\right)$ ?

• A. $\frac{G{R}^2}{g}$
• B. $\frac{R^{2}g}{G}$
• C. $g^2\frac{R}{G}$
• D. $\frac{GR}{g}$

Answer 1

The correct option is B $\frac{R^{2}g}{G}$

From Newton's law of gravitation,
the force of gravitation is

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

Let the $m_1=m$ be the mass of body
$m_2=M$ be the mass of earth

Thus, the Force experienced by the body is

$F=\frac{GMm}{R^2}$

Now near the surface of earth, acceleration due to gravity is $g$,

$\Rightarrow a=\frac{F}{m}$

$\Rightarrow g=\frac{GMm}{m{R}^2}$

$\therefore M=\frac{g{R}^2}{G}$

Hence, option $\left(b\right)$ is the correct answer.

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