Question

you weight 650 N. What would you wieght if the Earth were four times as massive as it is and its raduis were three times its present value?

Answer 1

To solve this problem we will apply the concept given by the law of gravitational attraction, which properly defines gravity under the function

$g = \frac{GM}{r^2}$

Here,

G = Gravitational Universal Constant

M = Mass of Earth

r = Distance between the human and the center of mass of the Earth

The acceleration due to gravity when is 4 times the mass of Earth and 3 times the radius would be given as,

$g_1 = \frac{GM}{r^2}$

$g_2 = \frac{G(4M)}{(3r)^2}$

$g_2 = \frac{4GM}{9r^2}$

$g_2 = \frac{4}{9} g_1$

The weight is defined as

$W = mg_1$

So the new weight would be given as

$W' = mg_2$

$W' = m(\frac{4}{9} g_1 )$

$W' = \frac{4}{9} mg_1$

$W' = \frac{4}{9} W$

$W' = \frac{4}{9}(650)$

$W' = 288.8N$

Therefore the weight under this condition is 288.8N