Question

Why is the weight of an object on the moon `1/6th`  its weight on the earth?

Answer 1

• The weight of an object on the earth is the force with which the earth attracts that object. Similarly, 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 which the moon exerts less attractive force on objects. The value of the acceleration due to gravity on the moon is `1/6` times the value of the acceleration due to gravity on the earth.
• Therefore, the weight of the object on the moon is `1/6` times the weight on the earth.

We have, g = `(GM)/R^2` and W = mg

The weight of a body of mass m on Earth is

W_e = mg_e

= `m(GM_e)/R_e^2`

The weight of a body of mass m on the moon is

`W_m = mg_m = (mGM_m)/R_m^2`

or `W_m/W_e = M_m/R_m^2 xx R_e^2/M_e`

As the mass of the moon M_m is `1/100` times the mass of the earth M_e and the radius of the moon R_m is `1/4` times.

The radius of earth R_e.

∴ `W_m/W_e = M_m/M_e (R_e/R_m)^2`

= `1/100 xx (4)^2 ≅ 1/6`