The mass of the earth is 6 × 10²⁴ kg and that of the moon is 7.4 ×10²² kg. If the distance between the earth and the moon be 3.84 × 10⁵ km, calculate the force exerted by the earth on the moon. (G = 6.7 × 10⁻¹¹Nm² kg⁻²)

Academic Physics NCERT Class 9

Mass of the Earth $(m_1)=6\times10^{24}\ kg$.

Mass of the Moon $(m_1)=7.4\times10^{22}\ kg.$

Distance between the Earth and the Moon$(r)=3.84\times10^{5}\ km$.

$=3.84\times10^{8}\ m$.

Gravitational Constant$(G)=6.7\times10^{-11} Nm^{2}/kg^{2}$.

Using Newton's law of Gravitation,

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

$F$ is the gravitational force between the Earth and the Moon.

On substituting the Given Values in the Formula,

Therefore, $F=\frac{(6.7\times10^{-11}\times6\times10^{24}\times7.4\times10^{22}}{(3.84\times10⁸)^{2}}$

Or $F=\frac{(6.7\times6\times7.4\times10^{19})}{(14.7456)}$

Or $F=20.1741\times10^{19}\ N$

Or $F ≈ 2.02\times10^{20}\ N$

Thus, the Gravitational Force of Attraction between the Earth and the Sun is $2.02\times10^{20}\ N$.

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Updated on: 10-Oct-2022

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