Question

The escape velocities from the surface of two planets of same masses is in the ratio of 1:2. Then ratio of their densities is:

• A. 1:2
• B. 1:4
• C. 1:8
• D. 1:16

Answer 1

The correct option is D 1:16

$V_{escope}=\sqrt{2gR}=\sqrt{\frac{2GM}{R}}$

$\frac{V_1}{V_2}=\sqrt{\frac{R_2}{R_1}}=\frac{1}{2}\Rightarrow \frac{R_2}{R_1}=\frac{1}{4}$

$\rho =\frac{m}{v}\Rightarrow \rho \alpha \frac{1}{r^2}$

$\frac{{\rho }_1}{{\rho }_2}={\left(\frac{R_1}{R_2}\right)}^2={\left(\frac{1}{4}\right)}^2=\frac{1}{16}$

${\rho }_1:{\rho }_2=1:16$

Hence,

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