Respuesta :

mberisso

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:

[tex]F_g=G\,\frac{m_1*m_2}{d^2}[/tex]

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:

[tex]Weight=G\frac{M*m}{R^2}[/tex]

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:

[tex]Weight=G\frac{M*m}{r^2}[/tex]

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.

Every particle follows the Universal Law of Gravitation. Our weight will increase when radius of The Earth decreased, with no change in mass.

The Universal Law of Gravitation:

Every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

[tex]\rm \bold { F = G \frac{m1 m2 }{d^2} }[/tex]

From the formula we can see here The gravitational force is inversely proportional to the distance ( radius of the earth)

When radius of the earth decreased, this increase the gravity.

Hence, we can conclude that our weight will increase when radius of Earth decreased, with no change in mass.

To know more about gravity refer to the  link:

https://brainly.com/question/21454806

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