Weight of an object on the moon

The weight of an object on the earth is the force with which the earth attracts the object. In the same way, the weight of an object on the moon is the force with which the moon attracts that object. The mass of the moon is less than that of the earth. Due to this the moon exerts lesser force of attraction on objects.

Let the mass of an object be m. Let its weight on the moon be W_m. Let the mass of the moon be M_m and its radius be R_m.

By applying the universal law of the gravitation, the weight of the object on the moon will be

W_m = G M_m × m/R²_m

Let the weight of the same object on the earth W_e. The mass of the earth is M and its radius is R.

W_e = G M × m/R²

W_m = G 7.36 × 10²² kg × m/ (1.74 × 10⁶m)²

Wm = 2.431 × 10¹⁰ × G × m…………………………………………..(1)

and W_e = 1.474 × 10¹¹ G × m…………………………………………..(2)

Dividing equation 1 by 2

W_m/W_e = 2.431 × 10¹⁰/ 1.474 × 10¹¹

or W_m/W_e = 0.165 ~_~ 1/6

Weight of the object on the moon/Weight of the object on the earth = 1/6

Weight of the object on the moon = (1/6) × its weight on the earth.

Example:- Mass of an object is 10 kg. What is its weight on the earth?

Solution:- mass (m) = 10 kg

Acceleration due to gravity (g) = 9.8 m s^-2

W = m × g

W = 10 kg × 9.8 m s^-2 = 98 N

Thus, the weight of the object is 98 N.