Question

You weigh 760 N.
What would you weigh if the Earth were six
times as massive as it is and its radius were
four times its present value?
Answer in units of N.

Answer 1

We can find the weight from the formula:

$$W = mg = m \dfrac{GM_E}{r_E^2} \propto \dfrac{M_E}{r_E^2} ,$$

here, $W$ is the weight of the person, $m$ is the mass of the person, $g$ is the acceleration due to gravity, $G$ is the gravitational constant, $M_E$ is the mass of the Earth, $r_E$ is the radius of the Earth.

Then, we can find the new weight of the person on the Earth which six times as massive as it is and its radius is four times its present value:

$$\dfrac{W_{new}}{W} = \dfrac{\dfrac{M_{E,new}}{(r_{E,new})^2}}{\dfrac{M_E}{r_E^2}} = \dfrac{\dfrac{6M_{E,new}}{(4r_{E,new})^2}}{\dfrac{M_E}{r_E^2}} = \dfrac{6}{(4)^2} = \dfrac{3}{8}.$$

Then, we calculate $W_{new}$:

$$W_{new} = \dfrac{3}{8}W = \dfrac{3}{8} \cdot 760N = 285N.$$

Answer:

$W_{new} = 285N.$