find gravitational force

Question

A planet has ? the density of earth but 2x the radius. find the surface gravitational force on this planet. (Hint: Earth’s is 10N/Kg)

Answer 1

Earth Gravitation force is 10N/kg = G *  M / r^2

Where M is the Mass of the earth and r is the radius of the earth.

 

The earths mass can be defined as

M = d * 4/3 * Pi * r ^3

The mass of the new planet is

Mn = d * 4/3 * pi * (2r)^3

The new planets gravitational force is

G * Mn / (2r)^2 = G d * 4/3 * pi * (2r)^3/(2r)^2

Putting a ratio of the new planet to Earth

the G, d, 4/3 and pi all cancel  so the ratio is

(2r)^3/((2r)2 / r^3/r^2 = 2

so the gravitational force on the new planet would be twice that on the earth or 20N/kg