Question

If $M$ is the mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is:

• A. $\frac{R^2}{M}$
• B. $\frac{M}{R^2}$
• C. $M{R}^2$
• D. $\frac{M}{R}$

Answer 1

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

Let us consider a body of mass m on surface of earth.

Gravitational force on it $F=mg$

By Newton's law of gravitation $F$ is also $G\frac{Mm}{R^2}$

So $mg=G\frac{Mm}{R^2}$
$\therefore$ On rearranging, $\frac{g}{G}=\frac{M}{R^2}$

Thus, option B is correct.