Question

The free-fall acceleration at the surface of planet 1 is 20 m/s2. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2?

Short answer

The value of g on planet 2 is : 10 m/s²

Step-by-step solution

Given Information

The free-fall acceleration at the surface of planet 1 is 20 m/s2

The radius and the mass of planet 2 are twice those of planet 1

Explanation

The free fall acceleration is calculated as below

$g=\frac{GM}{r^2}$​

g= acceleration due to gravity,

M =mass

G = universal gravitational constant

r= distance from the center of mass of body

role="math" localid="1649255660263" $$\begin{gathered} \frac{g^{\text{'}}}{g}=\frac{Gm}{r^2}·\frac{R^2}{GM} \\ {g}^{\text{'}}=g\frac{\left(2M\right)}{(2R{)}^2}\frac{R^2}{M} \\ {g}^{\text{'}}=\frac{g}{2} \end{gathered}$$

Substitute the value

$g^{\text{'}}=\frac{20\mathrm{m}/{\mathrm{s}}^2}{2}=10\mathrm{m}/{\mathrm{s}}^2$