The acceleration due to gravity at the surface of a planet is given by 2
R
GM
g = , where M and R
are the mass and radius of the planet respectively, and G is the gravitational constant.
It is given that
g = 10 N / kg
G = 7 × 10 –11 N m2 / kg 2
R = 6 × 10 6 m
What is M, correct to one significant figure?

Answer:

16) A

g = GM
R²

gR² = GM

M = gR²
G

Substituting the values,

M = 10 x (6 x 10⁶)²
7 x 10⁻¹¹

M = 10 x 36 x 10¹
7 x 10⁻¹¹

M = 36 x 10¹³
7 x 10⁻¹¹

M = 36 x 10 ¹³⁻⁽⁻¹¹⁾
7

M = 36 x 10²⁴
7

M = 5.15 x 10²⁴ ≈ 5 x 10²⁴