Question

The mass of the earth is $6.00\times {10}^{24}kg$ and that of the moon is $7.40\times {10}^{22}kg$. The constant of gravitation $G=6.67\times {10}^{-11}N{m}^{2}k{g}^{-2}$. Calculate gravitational force of attraction.

• A. $38\times {10}^{18}$
• B. $20.2\times {10}^{19}$
• C. $7.60\times {10}^8$
• D. $1.90\times {10}^8$

Answer 1

The correct option is B. $20.2\times {10}^{19}$

Given conditions

Mass of earth $\left(m_1\right)=6\times {10}^{24}kg$

Mass of moon $\left(m_2\right)=7.4\times {10}^{22}kg$

Distance between earth and the moon $\left(d\right)=3.84\times {10}^{5}km$

Gravitational constant $\left(G\right)=6.7\times {10}^{-11}{Nm}^2/kg$

Using Newton's law of gravitational $F=G\frac{m_1{m}_2}{d^2}$

$F$ is the force of gravitational between earth and moon

Substituting values in formula

$F=\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 7.4\times {10}^{22}}{{(3.84\times {10}^8)}^2}$

$\Rightarrow F=20.1741\times {10}^{19}N$

$\Rightarrow F=20.2\times {10}^{19}N$

Thus the gravitational force of attraction between the earth and moon is $20.2\times {10}^{19}N$.