Question

If the mass of an unknown planet is half the mass of the earth and its radius is twice that of earth, then find the weight of an object on its surface which weights 400N

Answer 1

weight of the object on earth, W = 400 N

so, its mass will be, m = W/g = 400/10 = 40 kg

now, we know that the acceleration due to gravity is given as

g = GM / R²

now, the acceleration due to gravity on te surface of the planet will be

g' = GM' / R'²

it is given

m' = M/2

and

R' = 2R

so, we get

g' = G(M/2) / 2R

or

g' = GM/4R = g/4

thus,

g' = 2.5 m/s

now, the weight of the body on the planet will be

W' = mg' = 40 kg X 2.5 m/s

or

W' = 100 N