Question

When two bodies are separated by certain distance, the gravitational force between then is F. If distance is increased by $100\%$, then gravitational force becomes--

• A. $\frac{F}{4}$
• B. $4F$
• C. $\frac{F}{2}$
• D. $2F$

Answer 1

The correct option is A $\frac{F}{4}$

As per Newton's law of gravitation, each particle attracts every other particle by the force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$F=\frac{G{m}_1\times m_2}{r^2}$

Here G is gravitational constant.

Now if the distance is increased by 100% means that it gets double. Therefore

$F_1=\frac{G{m}_1{m}_2}{(2r{)}^2}$

$F_1=\frac{1}{4}\times \frac{G{m}_1{m}_2}{r^2}$

$F_1=\frac{1}{4}\times F$.