Question

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.
What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth?

a) g/8 b) g/4 c) g/16 d) 2g

Answer 1

Option A is the correct answer.

Explanation:

Acceleration due to gravity

                  $g=\frac{GM}{r^2}$

         G = 6.67 × 10⁻¹¹ m² kg⁻¹ s⁻²

  Let mass of earth be M and radius of earth be r.

  We have

               $g=\frac{GM}{r^2}$

Now

         A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth.

       Mass of hypothetical planet, M' = M/2

       Radius of hypothetical planet, r' = 2r

  Substituting

              $g'=\frac{GM'}{r'^2}\\\\g'=\frac{G\times \frac{M}{2}}{(2r)^2}\\\\g'=\frac{\frac{GM}{r^2}}{8}\\\\g'=\frac{g}{8}$

Option A is the correct answer.