Question

A hypothetical planet has density , radius R, and surface gravitational acceleration g. If the radius of the plant were doubled, but the planetary density stays the same, the acceleration due to gravity at the surface would be:

Answer 1

The formula of acceleration due to gravity is given by

g= G*M/R^2 where M be the mass of the planet and R be the radius of the planet.

Multiply the numerator and denominator of right hand side expression with 4/3*pi*R, we get

g= 4/3*pi*R*G*M/(4/3*pi*R^3)

We know that 4/3*pi*R^3 is the volume of spherical planet, V. So,

g= 4/3*pi*R*G*M/V

g=4/3*pi*R*G*d ( because M/V=d, density of planet)

According to the question, the radius of the planet is doubled keeping density same. So,

g'= 4/3*pi*2R*G*d

g'= 2*g  (because g= 4/3*pi*R*G*d)

Therefore, the acceleration due to gravity at the surface would get doubled.