Question

If Earth's mass was cut in half, what would happen to your mass? Group of answer choices
decrease because gravitational force decreases
increase because gravitational force increases
decrease because gravitational force increases
nothing, mass is not affected by gravitational force

Answer 1

Answer:

nothing, mass is not affected by gravitational force

Explanation:

Weight is the gravitational force a planet exerts on a mass on the surface.

It is the product of the mass of an object with the gravitational acceleration that the planet produces.

The weight is the gravitational force

$W=mg$

where,

m = Mass of the object

g = Acceleration due to gravity = 9.81 m/s²

Mass is the property that matter has which opposes the force being applied to it. It is intrinsic to the object itself and does not change according to the gravitational force. But, the weight changes.

Answer 2

The correct statement is nothing, mass is not affected by gravitational force.

The gravitational force of attraction of every object in the universe is given by Newton's gravitational law;

$F_1= \frac{GmM_e}{R^2}$

where;

m is your mass

$M_e$ is mass Earth

R is the radius of the Earth

G is gravitational constant

If the mass of the Earth is cut into half, the gravitational force will be affected as follows;

$F_2= \frac{Gm}{R^2}\times \frac{M_e}{2} =\frac{1}{2} (\frac{GmM_e}{R^2}) = \frac{1}{2} (F_1)$

The gravitational force will be reduced by 2

Now, let's check how your mass will be affected;

$F_2= \frac{GmM_e}{R^2}\\\\GmM_e = F_2R^2\\\\m = \frac{F_2R^2}{G M_e} \\\\When, M_e \ is \ halved \ (0.5M_e) , \ F_2 = \frac{1}{2} F_1 = 0.5F_1\\\\m = \frac{0.5F_1R^2}{G \times 0.5M_e}\\\\m = \frac{F_1R^2}{G M_e}$

Your mass is not affected.

Thus, gravitational force is affected by mass but mass is not affected by gravitational force.

The correct statement is nothing, mass is not affected by gravitational force.

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