Question

If a planet existed where mass and radius both were half of those of earth what will be the value of acceleration due to gravity on the surface as compared to what is on the earth's surface?

Answer 1

1.As we know, acceleration due to gravity $g=GM/R^2$

where,

G= universal gravitational constant

M = mass of the body

R = radius of the body

2.Let, $g=GM/R^2$ ……….(i)

$g\text{'}=GM\text{'}/R{\text{'}}^2$ ………..(ii)

where,

$$\begin{gathered} M\text{'}=M/2 \\ R\text{'}=R/2 \end{gathered}$$

3.We have to put the value of M' and R' in equation (ii).

We get,

$$\begin{gathered} g\text{'}=\frac{(GM/2)}{{(R/2)}^2} \\ \frac{g}{g\text{'}}=(GM/R^2)/GM/2/{(R/2)}^2=1/2 \\ \frac{g}{g\text{'}}=1/2 \\ 2g=g\text{'} \end{gathered}$$

Hence , g' = 2g is the correct answer.