Question

Show that the weight of an object on the moon is $1/6th$ of its weight on the earth.

Answer 1

Step 1: Suppose an object of mass $\text{'}m\text{'}$

Let its weight on the moon be $\text{'}{W}_m\text{'}$

The mass of moon$=M$

The radius of moon$=R$

Gravitational constant$=G$

Step 2: Applying universal law of gravitation, the weight of the object on moon will be

weight on moon,$W_m=\frac{G\times Mm}{R^2}$ …… (i)

The weight of the same object on the earth $=W_e$

Mass of earth$=100M$ (as mass of earth is $100$ times than that of moon)

Radius of earth$=4R$ (as radius of earth is $4$ times than that of moon)

Step 3: Applying universal law of gravitation, the weight of the object on the earth will be:

weight on earth$W_e=\frac{G\times 100M\times m}{{\left(4R\right)}^2}$

$W_e=\frac{G\times 100M\times m}{16R^2}$ …… (i)

Dividing eq(i) and eq (ii), we get:

$\frac{W_m}{W_e}=\frac{{\displaystyle \frac{G\times M\times m}{R^2}}}{{\displaystyle \frac{G\times 100M\times m}{16R^2}}}$

$$\begin{gathered} \frac{W_m}{W_e}=\frac{G\times M\times m\times 16R^2}{R^2\times G\times 100M\times m} \\ \frac{W_m}{W_e}=\frac{16}{100} \\ \frac{W_m}{W_e}=\frac{1}{6} \\ \frac{Weightonmoon}{Weightonearth}=\frac{1}{6} \\ Weightonmoon=\frac{1}{6}weightonearth \end{gathered}$$

Thus, the weight of an object on the moon is $1/6th$ of its weight on the earth.