Question

The ratio between masses of two planets is 2 : 3 and the ratio between their radii is 3 : 2. The ratio between acceleration due to gravity on these two planets is:

• A. 4 : 9
• B. 8 : 27
• C. 9 : 4
• D. 27 : 8

Answer 1

Answer: (B)

8 : 27

acceleration due to gravity on the first planet

$g_1=\frac{G{M}_1}{{R_1}^2}$

acceleration due to gravity on the first planet

$g_1=\frac{G{M}_1}{{R_1}^2}$

$\frac{g_1}{g_2}=\frac{M_1}{M_2}\times \frac{{R_2}^2}{{R_1}^2}$

$=\frac{2}{3}\times {\left(\frac{2}{3}\right)}^2$

$=\frac{8}{27}$

Hence,

option $\left(B\right)$ is correct answer.