Question

The weight of an object on the surface of moon is _______ of the weight of object on the surface of the earth.

Answer 1

1. Acceleration due to gravity: Acceleration due to gravity by the earth is the acceleration achieved by any object due to the gravitational force of attraction by any planet.
2. Because each planet has a distinct mass and radius, each planet's gravitational acceleration will be different.
3. The mass of the moon is $\frac{1}{100}$times and the radius of the moon $\frac{1}{4}$times that of the earth.

Weight on Earth:

$W_e=G\frac{M_{e}m}{{R_e}^2}$

Weight on Moon:

$W_m=G\frac{M_{m}m}{R_m^2}$

Dividing the value of weight on Moon by weight on Earth,

$\frac{W_m}{W_e}=G\frac{M_{m}m}{R_m^2}\times \frac{R_e^2}{G{M}_{e}m}$

$$\begin{gathered} =\frac{M_m}{M_e}\times \frac{R_e^2}{R_m^2} \\ =\frac{M_m}{100M_m}\times \frac{{\left(4R_m\right)}^2}{{\left(R_m\right)}^2} \\ =\frac{16}{100} \\ =\frac{1}{6} \end{gathered}$$

$\text{weight of any object on the Moon}=\frac{1}{6}\text{weight of any object on the earth surface}$

Thus, the weight of an object on the surface of the moon is $\frac{\mathbf{1}}{\mathbf{6}}$ of the weight of an object on the surface of the earth.