Question

If the mass of the Earth somehow increased with no change in radius, your weight would

increase also
decrease
stay the same

Answer 1

Increases also.

The force due to gravity is given by,

F = GM.m/r²

Where G is a constant of proportionality

∴ F ∝ M.m/r²

When r remains constant, force due to gravity, F, will be;

F ∝ M.m

Where M is the mass of the earth and m is your mass

Since your mass does not change, we are going to have;

F ∝ M.

This means the weight F is directly proportional to the mass of the earth. when it increases the your weight also increases.

Answer 2

increase also

Step-by-step explanation:

The weight of a person is equal to the gravitational pull exerted by the Earth on the person:

`F=G(mM)/(R^2)`

where

`G=6.67\cdot 10^(-11) m^3 kg^(-1) s^(-2)` is the gravitational constant

`M` is the mass of the Earth

`m` is the mass of the person

`R` is the Earth's radius

We notice that the weight is directly proportional to the mass of the Earth. Therefore, if the mass of the Earth M increases, and the radius R does not change, the weight of the person increases as well.