Question

Planets A and B have same average density. Radius of A is twice that of B The ratio of acceleration due to gravity on the surface of A and B is

• A. 2:1
• B. 1:2
• C. 1:4
• D. 4:1

Answer 1

Answer: (A)

2:1

$\frac{V_{e_1}}{V_{e_2}}=\frac{\sqrt{\frac{2G\frac{4}{3}\pi {R_1}^3\rho }{R_1}}}{\sqrt{\frac{2G\frac{4}{3}\pi {R_2}^3\rho \sqrt{}}{R_2}}}$

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

$\sqrt{\frac{4R^2}{R^2}}=\frac{2}{1}$

Hence,

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