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f. The masses of the earth and moon are 6 x 1024 kg and 7.4x1022kg, respectively. The distance between them is 3.84 x 105 km. Calculate the gravitational force of attraction between the two? Use G = 6.7 x 10-11 N m2 kg-2  ?

 

in Chapter 1: Gravitation by Expert (11.5k points) | 92 views

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

Solution::
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.
⇒F= 2.02× 1020 N.
Thus, the Gravitational Force of Attraction between the Earth and the Sun is F= 2.02× 1020 N.

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