Question

A body on the surface of a planet with the same radius as Earths weighs 10 times more than it does on Earth. What is the mass of this planet in terms of Earths mass?

Answer 1

Answer:

Explanation:

Given

radius of Planet is equal to radius of Earth

$r_p=r_e$

Weight of body on Planet $F_p=mg_p$

where m=mass of body

$g_p=acceleration\ due\ to\ gravity\ on\ surface\ of\ Planet$

Weight of body on earth $F_e=mg_e$

$g_e=acceleration\ due\ to\ gravity\ on\ Earth$

acceleration due to gravity is given by

$g=\frac{GM}{r^2}$

where G=gravitational constant

M=mass of Planet

r=radius of planet

for earth $g_e=\frac{GM_e}{r_e^2}$

for planet $g_p=\frac{GM_p}{r_p^2}$

substituting these values in $F_e$ and $F_p$

$F_p=m\times \frac{GM_p}{r_p^2}---1$

$F_e=m\times \frac{GM_e}{r_e^2}---2$

divide 1 and 2

$\frac{F_p}{F_e}=\frac{m\times \frac{GM_p}{r_p^2}}{m\times \frac{GM_e}{r_e^2}}$

$10=\frac{M_p}{M_e}$

$M_p=10M_e$