Question

The ratio between masses of two planets is $3:5$ and the ratio between their radii is $5:3$. The ratio between their acceleration due to gravity will be

• A. $\frac{9}{25}$
• B. $\frac{25}{9}$
• C. $\frac{125}{27}$
• D. $\frac{27}{125}$

Answer 1

The correct option is D $\frac{27}{125}$

$9=\frac{Gm}{R^2}$

$\Rightarrow \frac{9_1}{9_2}=\frac{m_1}{m_2}\frac{R_2^2}{R_1^2}$

given that $\frac{m_1}{m_2}=\frac{3}{5}$

& $\frac{R_1}{R_2}=\frac{5}{3}$

So $\frac{9_1}{9_2}=\frac{3}{5}\times {\left(\frac{3}{5}\right)}^2=\frac{27}{125}$