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The mass of the earth is 6 × $10^{24}$ kg and that of the moon is 7.4 × $10^{22}$ kg. If the distance between the earth and the moon is 3.84 × $10^{5}$ km, calculate the force exerted by the earth on the moon (G = 6.67 × $10^{- 11}$ N $m^{2} {kg}^{- 2}$ ).

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2 ×

10^{20}

2.8 ×

10^{20}

4 ×

10^{20}

4.6 ×

10^{20}

answer is A.

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Detailed Solution

Given that, Mass of the earth,

M_{e}

= 6 ×

10^{24}

kg
Mass of the moon,

M_{m}

= 7.4 ×

10^{22}

kg
Distance between earth and moon, r = 3.84 ×

10^{5}

km = 3.84 ×

10^{8}

m
Gravitational force, G = 6.67 ×

10^{- 11}

m^{2} {kg}^{- 2}

Now, we know that force, F =

\frac{G M_{e} M_{m}}{r^{2}}

⸫ F =

\frac{6.67 \times 10^{- 11} \times 6 \times 10^{24} \times 7.4 \times 10^{22}}{(3.84 \times 10^{8})^{2}}

= 2 ×

10^{20}

N
So, the force exerted by the earth on the moon is 2 ×

10^{20}

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