Show that the weight of the …

The weight of an object on the moon will be about one-sixth of what is on the earth. Thus, a spring balance which shows the weight of a body to be 6 N on earth will show a weight of only 1 N when taken to the moon. The weight of an object on the moon is less than that on the earth because the mass and radius of the moon are less than that of earth.

Suppose we have an object of mass m. let its weight on the moon be W_m, the mass of the moon is M_m and its radius is R_m. now, according to the universal law of gravitation, the weight of the object on the moon will be:

W_m = G x M_m x m/R_m²

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

W_e = G x M x m/R²

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

W_m = 2.431 x 10¹⁰ G x m                                                                                               i.

W_e = 1.474 x 10¹¹ G x m                                                                                                ii.

Dividing both the equations i. & ii.

W_m/W_e = 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.