Question

Imagine a new planet having the same density as that of Earth but is $3$ times bigger than the Earth in size. If the acceleration due to gravity on the surface of Earth is g and that on the surface of the new planet is g', then:

• A. $g^{\prime }=3g$
• B. $g^{\prime }=\frac{g}{9}$
• C. $g^{\prime }=9g$
• D. $g^{\prime }=27g$

Answer 1

The correct option is A $g^{\prime }=3g$

$g_e=\frac{GM}{r^2}$ and $g_p=\frac{G{M}^{\prime }}{r^2}$ [ $R_p=3R_e$]

$g=\frac{G4\pi r^3}{3r^2}$

$g\propto r$

So,

$g_e=\frac{G4\pi r_e^3}{3r_e^2}$

$g_p=\frac{G4\pi r_p^3}{3r_p^2}$

$g_e=g$

Therefore $\frac{g_p}{g_e}$ = $\frac{3r}{r}$ i.e g' = 3g