Question

If the distance between two objects is doubled, then the gravitational force between them is reduced to $\frac{1}{8}$th of the original value of force.

• A. True
• B. False

Answer 1

The correct option is B False

Given

The distance between two objects is doubled.

Required to find

The gravitational force between the two objects

Solution

Let the masses of the two bodies be m₁ and m₂. Distance between them is r.

The gravitational force of attraction (g) between the two objects is given by $g=\frac{G{m}_1{m}_2}{r^2}$.

If the distance is doubled, then it is represented by 2r.

The gravitational force of attraction (g') after the distance is doubled is given by $g\text{'}=\frac{G{m}_1{m}_2}{{\left(2r\right)}^2}$.

$\Rightarrow g\text{'}=\frac{G{m}_1{m}_2}{{4r}^2}=\frac{1}{4}\times g=\frac{1}{4}thoftheoriginalvalue$

Hence, the given statement is false.