The gravitational pull between two bodies is 20N. Find the gravitational pull when their distance of separation is doubled.

1. Analyze the Question

We are given the initial gravitational force between two bodies and asked to find the new force when the distance between them is doubled. This is a classic application of Newton's Law of Universal Gravitation.

2. Explain the Concept

Newton’s Law of Universal Gravitation states that the force ($F$) between two bodies is directly proportional to the product of their masses ($m_1$ and $m_2$) and inversely proportional to the square of the distance ($r$) between them:

From this formula, we can see that $F \propto \frac{1}{r^2}$. This means if the distance $r$ changes, the force $F$ changes by the square of that factor.

3. Show the Solution

• Initial state: $F_1 = 20\text{N}$ at distance $r_1 = r$.
• Final state: $r_2 = 2r$ (the distance is doubled).

Using the proportionality $F \propto \frac{1}{r^2}$:

Substitute the values:

The $r^2$ terms cancel out:

Now, solve for $F_2$:

4. Identify the Answer

The calculation shows that when the distance is doubled, the force becomes one-fourth of the original value. Therefore, the correct option is B.

5. Exam Tip

Whenever you see "distance is doubled" in an inverse-square law problem (like Gravitation or Electrostatics/Coulomb's Law), remember the "Inverse Square Rule":

• If distance is doubled ($2r$), force becomes $1/2^2 = 1/4$ of the original.
• If distance is tripled ($3r$), force becomes $1/3^2 = 1/9$ of the original.
• If distance is halved ($1/2r$), force becomes $1/(1/2)^2 = 4$ times the original.