Question

The weight of an object is the same on two different planets. The mass of planet A is only sixty percent that of planet B. Find the ratio of Ra/Rb of the radii of the planets.

Answer 1

0.775

Step-by-step explanation:

The weight of an object on a planet is equal to the gravitational force exerted by the planet on the object:

`F=G(Mm)/(R^2)`

where

G is the gravitational constant

M is the mass of the planet

m is the mass of the object

R is the radius of the planet

For planet A, the weight of the object is

`F_A=G(M_Am)/(R_A^2)`

For planet B,

`F_B=G(M_Bm)/(R_B^2)`

We also know that the weight of the object on the two planets is the same, so

`F_A = F_B`

So we can write

`G(M_Am)/(R_A^2) = G(M_Bm)/(R_B^2)`

We also know that the mass of planet A is only sixty percent that of planet B, so

`M_A = 0.60 M_B`

Substituting,

`G(0.60 M_Bm)/(R_A^2) = G(M_Bm)/(R_B^2)`

Now we can elimanate G, MB and m from the equation, and we get

`(0.60)/(R_A^2)=(1)/(R_B^2)`

So the ratio between the radii of the two planets is

`(R_A)/(R_B)=√(0.60)=0.775`