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 = (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 = (GM)/(r^2)`

`g_2 = (G(4M))/((3r)^2)`

`g_2 = (4GM)/(9r^2)`

`g_2 = (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((4)/(9) g_1 )`

`W' = (4)/(9) mg_1`

`W' = (4)/(9) W`

`W' = (4)/(9)(650)`

`W' = 288.8N`

Therefore the weight under this condition is 288.8N