Question

The average distance between the earth and the moon is $3.84\times {10}^{5}km$. If the mass of moon is $7.4\times {10}^{22}kg$ and that of earth is $6\times {10}^{24}kg$, the gravitational force of the moon on the earth is:

• A. $2.01\times {10}^{20}N$
• B. $20.1\times {10}^{21}N$
• C. $20.1\times {10}^{20}N$
• D. none of the above

Answer 1

The correct option is A

$2.01\times {10}^{20}N$

Step 1: Given data

Mass of Earth, $m_1=6\times {10}^{24}kg$

Mass of moon, $m_2=7.4\times {10}^{22}kg$

Distance, $d=3.84\times {10}^{5}km=3.84\times {10}^{8}m$

Magnitude of force, $F=?$ (To be calculated)

Step 2: Calculating the magnitude of the force

Applying, $F=\frac{G\times m_1\times m_2}{d^2}$

$$\begin{gathered} \Rightarrow F=\frac{6.67\times {10}^{-11}N{m}^2/k{g}^2\times 6\times {10}^{24}kg\times 7.4\times {10}^{22}kg}{{(3.84\times {10}^{8}m)}^2} \\ \Rightarrow F=2.01\times {10}^{20}N \end{gathered}$$

Hence, the correct answer is option (A) i.e. $2.01\times {10}^{20}N$.