Question

The masses of the earth and moon are 6×10 raised to 24 kg and 7.4× 10 raised to 22 kg respectively. the distance between them is 3.84×10 raised to 5 km. calculate the gravitational force of attraction between the two? use G = 6.7×10 raised to negative 11 N m per square kg raised to negative square

Answer 1

$\textbf{Solution}$

$<b><i>Given$

Mass of the Earth(m₁) = 6 × 10²⁴ kg.

Mass of the Moon(m₂) = 7.4 × 10²² kg.

Distance between the Earth and the Moon(d) = 3.84 × 10⁵ km

 = 3.84 × 10⁸ m( 1km= 1000 m)

Gravitational Constant(G) = 6.7 × 10⁻¹¹ Nm²/kg².

Newton's law of Gravitation states that

$F = \dfrac{G \times \: M \times M \: }{ {d}^{2} }$

F = (6.7 × 10⁻¹¹ × 6 × 10²⁴ × 7.4 × 10²²) ÷ (3.84 × 10⁸)²

=> F = (6.7 × 6 × 7.4 × 10¹⁹) ÷ (14.7456)

$F = 2.01 \: \times {10}^{ 20} N \:$

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Answer 2

Answer:

20.2 × 10¹⁹ N

Explanation:

Given :

Mass of earth = 6 × 10²⁴ kg

Mass of moon = 7.4 × 10²² kg

Distance between them = 3.84 × 10⁵ km = 3.84  × 10⁸ m

We have value of G = 6.7 × 10⁻¹¹ N m² kg⁻²

We have to find force :

We have :

F = G m₁ m₂ / r²

F = ( 6.7 × 10⁻¹¹ ) ( 6 × 10²⁴ ) ( 7.4 × 10²² ) / (  3.84 × 10⁸ )² N

F = 20.2 × 10¹⁹ N

Hence force exerted by the earth on the moon is 20.2 × 10¹⁹ N.