Question

Two planets of equal radii have their masses in the ratio 1:2, then the ratio of their ‘g’ is:

• A. 1:4
• B. 1:2
• C. 4:1
• D. 2:1

Answer 1

The correct option is B 1:2

Let the mass of the first planet be $M_1$
Let the radius of the first planet be $R_1$
Let the mass of the second planet be $M_2$
Let the radius of the second planet be $R_2$
Since the radii of the two planets are equal,
$R_1$ = $R_2$ = $R$

Acceleration due to gravity is given by:
$g=\frac{GM}{R^2}$​

For the first planet, acceleration due to gravity is:
$g_1=\frac{G{M}_1}{R^2}$
For the second planet, acceleration due to gravity is:
$g_2=\frac{G{M}_2}{R^2}$

Taking the ratio,
$\frac{g_1}{g_2}=\frac{G{M}_1/R^2}{G{M}_2/R^2}$
$\frac{g_1}{g_2}=\frac{M_1}{M_2}$

It's given that, $M_2=2M_1$.
On substituting these in the expression, we get:
$\frac{g_1}{g_2}=\frac{1}{2}$