Question

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  ?

 

Answer 1

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.