Question

The earth is 4times the size of the moon and acceleration due to gravity of the earth is 80times that of the moon. Calculate the ratio of the mass of the moon to that of the earth.

Answer 1

Let's first write the weight of the Moon and Earth:

$$W_{Moon}=M_{Moon}g_{Moon},$$ $$W_{Earth}=M_{Earth}g_{Earth}=M_{Earth}80g_{Moon}.$$

Dividing $W_{Moon}$ by $W_{Earth}$, we get:

$$\dfrac{W_{Moon}}{W_{Earth}}=\dfrac{M_{Moon}g_{Moon}}{M_{Earth}80g_{Moon}},$$ $$\dfrac{W_{Moon}}{W_{Earth}}=\dfrac{M_{Moon}}{80M_{Earth}},$$ $$\dfrac{M_{Moon}}{M_{Earth}}\propto \dfrac{1}{80}.$$

Therefore, the ratio of the mass of the Moon to that of the Earth is 1:80.