Respuesta :
Answer:
[tex]\frac{\rho_A}{\rho_B} = 0.4[/tex]
Explanation:
As we know that the acceleration due to gravity on the surface of the planet is given as
[tex]a = \frac{GM}{R^2}[/tex]
so we will have
M = mass of the planet
[tex]M = \rho (\frac{4}{3} \pi R^3)[/tex]
so we have
[tex]a = \frac{G \rho \frac{4}{3} \pi R^3}{R^2}[/tex]
[tex]a = \frac{4}{3}\rho \pi G R[/tex]
so we have
[tex]\frac{a_A}{a_B} = \frac{\rho_A R_A}{\rho_B R_B}[/tex]
[tex]\frac{1}{10} = \frac{\rho_A (R_B/4)}{\rho_B R_B}[/tex]
[tex]\frac{1}{10} = \frac{\rho_A}{4\rho_B}[/tex]
[tex]\frac{\rho_A}{\rho_B} = 0.4[/tex]
