In order to determine which statements correctly describe the effect of distance on gravitational and electrical forces, let's analyze each force:
1. Gravitational Force:
- Gravitational force is described by Newton's Law of Universal Gravitation, which states that the force between two masses is proportional to the product of their masses and inversely proportional to the square of the distance between them.
[tex]\[
F_g = G \frac{m_1 m_2}{r^2}
\][/tex]
Here, [tex]\( F_g \)[/tex] is the gravitational force, [tex]\( G \)[/tex] is the gravitational constant, [tex]\( m_1 \)[/tex] and [tex]\( m_2 \)[/tex] are the masses, and [tex]\( r \)[/tex] is the distance between the centers of the masses.
- This indicates that the gravitational force decreases with the square of the distance between two objects but has an infinite reach; it never becomes zero regardless of the distance.
2. Electrical Force:
- The electrical force between two charges is described by Coulomb's Law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.
[tex]\[
F_e = k_e \frac{q_1 q_2}{r^2}
\][/tex]
Here, [tex]\( F_e \)[/tex] is the electrical force, [tex]\( k_e \)[/tex] is Coulomb's constant, [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the charges, and [tex]\( r \)[/tex] is the distance between the charges.
- This indicates that, similar to gravitational force, the electrical force decreases with the square of the distance between the charges but also has an infinite reach.
Now let's analyze each statement:
- The gravitational force has an infinite reach. (True)
- The electrical force has an infinite reach. (True)
- The gravitational force is inversely proportional to the distance. (False; it is inversely proportional to the square of the distance.)
- The electrical force is inversely proportional to the distance. (False; it is inversely proportional to the square of the distance.)
- The gravitational force is inversely proportional to the square of the distance. (True)
- The electrical force is inversely proportional to the square of the distance. (True)
Therefore, the correct statements are:
- The gravitational force has an infinite reach.
- The electrical force has an infinite reach.
- The gravitational force is inversely proportional to the square of the distance.
- The electrical force is inversely proportional to the square of the distance.
