The mass of earth is $6\times10^{24}\ kg$ and that of the moon is $7.4\times10^{22}\ kg$. If the distance between the earth and the moon is $3.84\times10^{5}\ km$. Calculate the force exerted by the earth and the moon.

Given,

Mass of the Earth $( m_1)=6\times 10^{24}\ kg$

Mass of the Moon $( m_2)=7.4\times 10^{22}\ kg$

Distance between the Earth and the Moon $( r)=3.84\times 10^5\ km= 3.84\times 10^8\ m$

And gravitational Constant $( G)=6.7\times 10^{-11}\ N-m^2/kg^2$



Using the Newton's law of Gravitation,

$F=G\frac{m_1.m_2}{r^2}$

$F$ is the Force of Gravitation exerted by the Earth and the Moon.

On substituting the Given Values in the Formula,

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

$F=\frac{6.7\times 6\times 7.4\times 10^{19}}{14.7456}$

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

$F=2.02\times 10^{20}\ N$      [approximately]

Thus, the force exerted by the Earth and the Sun is $2.02\times 10^{20}\ N$.

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Updated on: 10-Oct-2022

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