Question

Objects 1 and 2 attract eachother with a gravitational force

Answer 1

Given,

The force between object 1 and object 2, F₁=72.0 units

From Newton's law of gravitation, the gravitational force between two objects is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them.

Let us assume that initially, the distance between object 1 and object 2 was 'r'.

From Newton's law of gravitation,

`F_1\propto(1)/(r^2)`

After tripling the distance between the objects, the separation is 3r.

Again, from Newton's law of gravitation,

`\begin{gathered} F_2\propto(1)/((3r)^2) \\ \Rightarrow F_2\propto(1)/(9r^2) \end{gathered}`

On dividing the two forces,

`\begin{gathered} (F_2)/(F_1)=((1)/(9r^2))/((1)/(r^2)) \\ =(r^2)/(9r^2) \\ \Rightarrow F_2=(F_1)/(9) \end{gathered}`

On substituting the values of F₁,

`\begin{gathered} F_2=(72.0)/(9) \\ =8.0\text{ units.} \end{gathered}`

Thus after tripling the distance between object 1 and object 2, the new gravitational force is 8.0 units.