Question

The masses of earth and the moon are $6×10^{24} and 7.4×10^{22}$ kg respectively. The distance between them is 3.84×10^5 km. Calculate the gravitation force of attraction between the two? Use G = 6.7×10^-11 Nm^2Kg^-2.

Answer 1

$\mathbb{\purple{\huge{Heya\:Walkers!!}}}$

$<b><u>Answer</u></b>$

$<b><u>Step-by-step explanation</u></b>$

$<b>Given conditions,</b>$

Mass of Earth (m1) = $6×10^{24}$ kg

Mass of Moon (m2) = $6×10^{22}$ kg

Distance between the Earth and the Moon (d) = $3.84 × 10^5$ km

= $3.84 × 10^8$ km

Universal Gravitation Constant (G) = $6.7 × 10^{-11} Nm^2Kg^{-2}$

$<b>By using, Newton's law of gravitation,</b>$

$F = \frac{GMm}{d^2}$

Where, F is the force of gravitation between the Earth and the Moon.

Substituting the given values in thd above equation,

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

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

$F = 20.1741×10^{19}$

$F = (approx) 20.2×10^{19}$

$<b><u><font size="5">So, the gravitation force between the Earth and the Moon is 20.2×10^{19} </font></u></b>$

Thanks...!

With♥️

Answer 2

Hello Dear.

Here is the answer---

Given Conditions ⇒

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.

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

Using the Newton's law of Gravitation,

 F = G × m₁×  m₂ × /d².

F is the Force of Gravitation between the Earth and the Moon.

Substituting the Given Values in the Formula,

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

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

⇒ F = 20.1741 × 10¹⁹ N.

⇒ F ≈ 20.2 × 10¹⁹ N.

Thus, the Gravitational Force of Attraction between the Earth and the Sun is 20.2 × 10¹⁹ N.

Hope it helps.