Question

A man of 90 kg weighs 146 N on the moon. The radius of the moon is 1.74 × 106m. Find the mass of themoon.

Answer 1

7.36×10²² kg

Given the following data:

Mass of man = 90 kilograms

Weight of man = 146 newtons.

Radius of moon = 1.74×10^6 meters

Gravitational constant = 6.67×10^-11

To determine the mass of the moon:

First of all, we would calculate the acceleration due to gravity on the moon:

W=m×g

146=90×4

g=1.6 m/s²

From the law of gravitational force, we have the formula:

g=Gm/r²

Where:

g is the acceleration due to gravity.

G is the gravitational constant.

m is the mass of a planet.

r is the radius.

Making m the subject of formula, we have:

m=gr²/G

Substituting the given parameters into the formula, we have;

m=.6×(1.74×10^6)²/6.67×10^-11

m=4.84×10^12/6.67×10^-4

m=7.36×10²²