Question

Imagine a new planet having the same density as that of earth but it 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'=3g
• B. g'=$\frac{g}{9}$
• C. g'=9g
• D. g'=$\frac{g}{3}$

Answer 1

Answer: (A)

g'=3g

Answer 2

Let the mass and radius of the new planet be M′ and R′, then for same density as earth,
R′=3R
M′=27M
we know M$\propto$V, where V$\propto$R3
For Earth

g=$\frac{GM}{R^2}$ (1)

and for new planet

g'=$\frac{GM'}{R^2}$

=$\frac{G(27M)}{(3R)^2}$

=$3\bigg(\frac{GM}{R^2}\bigg)$=3g

$\Rightarrow$ g'=3g

Therefore, the correct option is (A): g'=3g