Question

The force with which the earth attracts an object is called the weight of the object. Calculate the weight of the moon from the following data : The universal constant of gravitation G = 6.67 × 11⁻¹¹ N−m²/kg², mass of the moon = 7.36 × 10²² kg, mass of the earth = 6 × 10²⁴ kg and the distance between the earth and the moon = 3.8 × 10⁵ km.

Answer 1

The force between the Earth and the Moon is given by $F=\frac{\mathrm{G}Mm}{r^2}$.
Here, M is the mass of the earth; m is the mass of the moon and r is the distance between Earth and Moon.

On substituting the values, we get:
$F=\frac{6.67\times {10}^{-11}\times 7.36\times {10}^{22}\times 6\times {10}^{24}}{3.8\times 3.8\times {10}^{16}}$

$$\begin{gathered} =\frac{6.67\times 7.36\times {10}^{35}}{(3.8{)}^2\times {10}^{16}} \\ =20.3\times {10}^{19}=2.03\times {10}^{20} \\ \approx 2.0\times {10}^{20}\mathrm{N} \end{gathered}$$

∴ The weight of the moon is $2.0\times {10}^{20}\mathrm{N}$.