Question

I the mass of a planet is $10\%$ less than that of the Earth and the radius $20\%$ greater than that of Earth, the acceleration due to gravity on the planet will be:

• A. $\frac{5}{8}$ times that on the surface of the Earth
• B. $\frac{3}{4}$ times that on the surface of the Earth
• C. $\frac{1}{2}$ times that on the surface of the Earth
• D. $\frac{9}{10}$ times that on the surface of the Earth

Answer 1

The correct option is A $\frac{5}{8}$ times that on the surface of the Earth

Given $m_p=\frac{9}{10}{m}_e$ & $r_e=\frac{12}{10}{r}_e$

$\Rightarrow g_e=\frac{G{M}_e}{{r_e}^2}$

$\Rightarrow g_p=\frac{G{M}_p}{{r_p}^2}=G\frac{9}{10}{m}_e\frac{10}{12}$

$=\frac{5}{8}{g}_e$