Question

The weight of a body on the surface of the Earth is 10 N. Find the weight of a body assuming it is on a planet whose mass is 10 times less than the mass of the Earth, and the radius of that planet is 2 times smaller than the radius of the Earth. (Answer: Gx = 3.99 N)

Answer 1

We can find the weight of the body on the Earth as follows:

$$W_E=mg_E=\dfrac{GM_Em}{R_E^2}.$$

Then, the weight of the body on the unknown planet will be:

$$W_p=mg_p=\dfrac{GM_pm}{R_p^2}=\dfrac{G0.1M_Em}{(\dfrac{1}{2}R_E)^2}=0.4W_E,$$ $$W_p=0.4\cdot10\ N=4\ N.$$