Question

A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 106 meters, find the mass of the moon.
a) 7.36 x 10^(28) kg
b) 2.4 x 10^(10) kg
c) 7.36 x 10^(22) kg
d) 1.43 x 10^(4) kg

Answer 1

Answer:

7.36 × 10^22 kg

Explanation:

Mass of the man = 90kg

Weight on the moon = 146N

radius of the moon =1.74×10^6

Weight =mg

g= weight/mass

g= 146/90 = 1.62m/s^2

From the law of gravitational force

g = GM/r^2

Where G = 6.67 ×10^-11

M = gr^2/G

M= 1.62 × (1.74×10^6)^2/6.67×10^-11

= 4.904×10^12/6.67×10^-11

=0.735×10^23

M= 7.35×10^22kg. (approximately) with option c

Answer 2

Answer: c) 7.36 x 10^(22) kg

The mass of the moon is 7.36 x 10^(22) kg

Explanation:

Given;

mass of the man on the moon, m=90kg

weight of the man on the moon, W=146 N,

radius of the moon, r=1.74×10^6 m.

Weight is the interaction of the mass and the gravity, so

W=mg.

g = W/m

Substituting the given values, we can find the gravity

g = 146/90 = 1.622m/s2

The acceleration due to gravity is the strength of moon's gravitational field, so

g=GM/r^2

M = gr^2/G ......2

where G is gravitational constant.

G = 6.67 × 10^-11

Substituting the values into eqn2, we have

M = 1.622 × (1.74×10^6)^2/6.67 ×10^-11

M = 7.362 × 10^22kg

M = 7.36 × 10^22kg