Question

Consider two spherical planets of same average density, Planet 2 is 8 limes as massive as planet 1. The ratio ot the acceleration due to gravity on the second planet to that on the first is.

• A. 1
• B. 2
• C. 4
• D. 8

Answer 1

The correct option is B 2

given mass of planet $A=m_A$
and mass of planet $B=m_B$
$m_B=8mA$

$g_A=\frac{G{m}_A}{r_{A^2}}$and$g_B=\frac{G{m}_B}{r_{B^2}}$
or $\frac{g_A}{g_B}=\frac{m_A}{m_B}{\left(\frac{r_B}{r_A}\right)}^2$ ........... (i)
$\because m_B=8m_A$
$\frac{4}{3}\pi r_B^{3}d=8\left(\frac{4}{3}\pi r_A^{3}d\right)\Rightarrow \frac{r_B}{r_A}=2$
$\frac{g_A}{g_B}=\frac{1}{8}\times 4=\frac{1}{2}$
$g_B=2g_A$