Question

The masses of two planet A and B are in the ratio 1 : 2 and their radius are in the ratio respectively. Then the ratio of acceleration due to gravity on the surface of planet A to B acceleration due to gravity on the surface of planet B will be.

• A. 1 : 2
• B. 1: 1
• C. 3 : 5
• D. 5 : 3

Answer 1

Answer: (B)

1: 1

Acceleration due to gravitational force on the surface of a planet is given by:

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

Thus if the masses and radii of two planets are in the same ratio of $1:2$, this gives

$\frac{g_A}{g_B}=\frac{M_A}{M_B}\times \frac{R_B^2}{R_A^2}=\frac{M_A}{M_B}\times {\left(\frac{R_B}{R_A}\right)}^2$

$\frac{g_A}{g_B}=\frac{1}{2}\times {\left(\frac{2}{1}\right)}^2$

$\frac{g_A}{g_B}=\frac{2}{1}$

Hence the ratio of acceleration due to gravity on the surfaces of planets A and B will be $2:1$