Question

Both the electrical force and the gravitational force between two objects share which relationship?

They are directly proportional to mass.
They are inversely proportional to the square of the distance.
They are inversely proportional to charge.
They are directly proportional to the square of the distance.

Answer 1

Answer : They are inversely proportional to the square of the distance.

Explanation :

We know that the electrical or electrostatic force is given by :

`F=(1)/(4\pi \epsilon_0)(q_1q_2)/(r^2)`.........(1)

Where,

`(1)/(4\pi \epsilon_0)` is constant

`q_1`
`q_2` are the electric charges,

r is the distance between two charges.

Similarly, the gravitational force is given by :

`F=G(m_1m_2)/(r^2)`..........(2)

Where

G is the universal gravitational constant

`m_1` and
`m_1` are the masses

r is the distance between them

From equation (1) and (2), it is clear that the both electrical as well as gravitational forces are inversely proportional to the square of the distance between them.

Hence, the correct option is (b) " They are inversely proportional to the square of the distance" .

Answer 2

They are inversely proportional to the square of the distance.

Step-by-step explanation:

The magnitude of the gravitational force between two objects is given by

`F=G(m_1 m_2)/(r^2)`

where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

The magnitude of the electrical force between two objects is given by

`F=k(q_1 q_2)/(r^2)`

where k is the Coulomb's constant, q1 and q2 are the charges of the two objects, and r is the distance between the two objects.

In both cases, we see that the magnitude of the force is iinversely proportional to the square of the distance,
`(1)/(r^2)`, so the correct option is

They are inversely proportional to the square of the distance.