Question

The force with which the earth attracts an object is
called the weight of the object. Calculate the weight of
the moon from the following data : The universal
constant of gravitation G = 6.67 x 10⁻¹¹ N-m²/kg², mass
of the moon = 7.36 x 10²² kg, mass of the earth
= 6 x 10²⁴ kg and the distance between the earth and the
moon = 3.8 x 10⁵ km.

Concept of Physics - 1 , HC VERMA , Chapter "The Force"

Answer 1

Hello Dear.

Given ⇒
Mass of the Earth(m₁) = 6 × 10²⁴ kg.
Mass of the Moon(m₂) = 7.36 × 10²² kg.
Gravitation Constant(G) = 6.67 × 10⁻¹¹ Nm²kg⁻².
Distance between the Earth and the Moon(r) = 3.8 × 10⁵ km.
= 3.8 × 10⁸ m.

Now, Using the Newton's law of Gravitation,

$F = G \frac{m_{1}m_{2}}{r^{2} }$
⇒ F = (6.67 × 10⁻¹¹ × 6 × 10²⁴ × 7.36 × 10²²) ÷ (3.8 × 10⁸)²
⇒ F = (294.5272/14.44) × 10¹⁹
⇒ F = 20.4 × 10¹⁹ N.
⇒ F ≈  2 × 10²⁰ N.


Hence, the Weight of the Moon or the Force by which the Earth attracts it is 2 × 10²⁰ N.


Hope it helps.

Answer 2

HEY!!

______________________________

✔The force between the Earth and the Moon is given by F=GMm/ r2.

✔Here, M is the mass of the earth; m is the mass of the moon and r is the distance between Earth and Moon.

✴SUBSTITUTION

▶F= 6.67×10−11×7.36×10^22×6×10^24 / 3.8×3.8×1016

▶6.67×7.36×10^35 / (3.8)^2×10^16

▶20.3×10^19=2.03×10^20≈2.0×1020 N

▶▶The weight of the moon is 2.0×1020 N.