1. ¿cómo se modifica la fuerza gravitatoria o eléctrica entre dos cuerpos en cada uno de los siguientes casos? explícalo.
a. la masa de uno de los cuerpos se cuadruplica.
b. se duplica la masa de uno de los cuerpos, al tiempo que se cuadruplica la distancia entre los cuerpos.
c. la carga de los dos cuerpos se duplica y se duplica la distancia entre los cuerpos.
d. una de las cargas se duplica y la distancia entre los cuerpos se reduce a la mitad.

Answers:

A) The gravitational force is four times stronger

B) The gravitational force is 1/8 weaker

C) The electric force remains the same

D) The electric force is eight times stronger

Explanation:

In this question we have to deal with two type of forces that depend on the inverse squared distance, Gravitational force  and Electrostatic force :

The first one is expressed according to the law of universal gravitation:

 (1)

Where:  

is the module of the attraction force exerted between both bodies  

is the universal gravitation constant.  

and are the masses of both bodies.  

is the distance between both bodies

As we can see, the gravity force is directly proportional to the mass of the bodies and inversely proportional to the square of the distance that separates them.

The second force is expressed by Coulomb's Law:  

 (2)

Where:

is the electrostatic force between two point charges

is a proportionality constant.

and  are point charges

the distance that separates both point charges

So, when two electrically charged bodies come closer, appears a force that attracts or repels them, depending on the sign of the charges of this two bodies.  

Having this clear, let's start with the answers according to each situation:

According to this situation, the law of universal gravitation equation is:

Rewritting:

This means the gravitational force between both masses is increased by 4.

In other words:

According to this situation, the law of universal gravitation equation is expressed as:

Simplifying:

This means the gravitational force changes by a factor of 1/8.

In other words:

According to this situation, Coulomb's law is expressed as:

Simplifying:

This means:

According to this situation, Coulomb's law is expressed as:

Simplifying:

This means the electric force is increased by 8.

In other words:

option number c is the right answer.

because if the tool that you are using is not balanced it there would be false mass.