Question

If the ratio of the masses of two planets is 2:3 and the ratio of their radii is 4:7 then the inverse ratio of their acceleration due to gravity will be

• A. 49:24
• B. 24:49
• C. 7:8
• D. 8:7

Answer 1

The correct option is B

24:49

Step 1: Given data

The ratio of the masses of the two planets is 2:3.

The ratio of their radii is 4:7.

Step 2: Calculate the inverse ratio of their acceleration due to gravity

The acceleration due to gravity on the first planet is

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

The acceleration due to gravity on the second planet is

$g_2=\frac{G{M}_2}{{R_2}^2}$

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

$\frac{g_1}{g_2}=\frac{2}{3}\times {\left(\frac{7}{4}\right)}^2$

Step 3: Final answer

$\frac{g_1}{g_2}=\frac{98}{48}=\frac{49}{24}$

The inverse ratio will be $\frac{24}{49}$.

Thus, the correct answer is (b).