Question

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

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.