Question

If $M$ is the mass of the earth and $R$ its radius, the ratio of the acceleration due to gravity 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

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

Step 1: Given data

$M\to$ mass of the earth

$R\to$ radius of the earth

We have to find the ratio of acceleration due to gravity and gravitational constant,$\frac{g}{G}$

Step 2: Formula and solution

We know, acceleration due to gravity is given by,

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

Ratio,

$$\begin{gathered} \frac{g}{G}=\frac{GM}{R^2}\times \frac{1}{G} \\ \Rightarrow \frac{g}{G}=\frac{M}{R^2} \end{gathered}$$

Therefore, the ratio of acceleration due to gravity and gravitational constant is $\frac{M}{R^2}$

Option B is correct