Question

3. If the radius of Earth decreased, with no change in mass, your weight would

Answer 1

Answer:

The weight of the person would increase

Explanation:

The Universal Law of Gravitation gives the magnitude of the force between the masses of two objects (m1 and m2) separated a given distance "d" as:

$F_g=G\,\frac{m_1*m_2}{d^2}$

where G is the universal gravitational constant.

Our weight on Earth is this force between the Earth (of mass M) and ourselves (our mass m) at a distance that is the Earth's radius R:

$Weight=G\frac{M*m}{R^2}$

Now, if we keep all the values equal (mass of the Earth M and our mass m) except for the distance between the center of the Earth and our center of gravity (the radius of the Earth), we are going to have now a smaller radius (r) in the formula above:

$Weight=G\frac{M*m}{r^2}$

and dividing by a smaller number (r is smaller than R), will render a larger quotient. This means that the actual force (weight) will become larger, so the weight would clearly increase.