Question

The mass of earth is $6\times {10}^{24}kg$ and that of the moon is $7.4\times {10}^{22}kg$. If the distance between earth and moon is $3.84\times {10}^{6}km$. Calculate the force exerted by the earth on the moon. $(G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2})$

• A. $6\times {10}^{24}N$
• B. $20\times {10}^{17}N$
• C. $36\times {10}^{24}N$
• D. $12\times {10}^{17}N$

Answer 1

The correct option is B $20\times {10}^{17}N$

Given, mass of earth $m_e=6\times {10}^{24}kg$

mass of moon $m_m=7.4\times {10}^{22}kg$

distance between earth and moon $r=3.84\times {10}^{6}km=3.84\times {10}^{9}m$

Gravitational constant $G=6.7\times {10}^{-11}N{m}^{2}k{g}^{-2}$

Using Newton's law of gravitation,

Force exerted by Earth on the Moon is given by,

$F=\frac{G{m}_e{m}_m}{r^2}=\frac{6.7\times {10}^{-11}\times 6\times {10}^{24}\times 7.4\times {10}^{22}}{(3.84\times {10}^9{)}^2}=20\times {10}^{17}N$