If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is

Question

If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is (A)  0.2 g  (B)  0.4 g  (C)  2 g  (D)  4 g

Tardigrade Admin · Accepted Answer

g=(4/3) π G R ρ and g '=(4/3) π G R ' ρ ∴ (g '/g) =(R '/R)=0.2 g ' =0.2 g

Q. If the density of a small planet is the same as that of earth, while the radius of the planet is $0.2$ times that the earth, the gravitational acceleration on the surface of that planet is

$0.2 g$

$0.4 g$

$2 g$

$4 g$

$g = \frac{4}{3} π GRρ$
and $g^{'} = \frac{4}{3} π G R^{'} ρ$
$∴ \frac{g ^{'}}{g} = \frac{R ^{'}}{R} = 0.2$
$g^{'} = 0.2 g$

Q. If the density of a small planet is the same as that of earth, while the radius of the planet is 0.2 times that the earth, the gravitational acceleration on the surface of that planet is

0.2g

0.4g

2g

4g