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

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: 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