Question

Two objects , A and B , are separated by a distance R. Object A exerts a gravitational force , F , on object B. What is the new gravitational force exerted if the mass of object A is tripled and the distance R is doubled ?

Answer 1

Given

Two objects , A and B , are separated by a distance R. Object A exerts a gravitational force , F , on object B.

To find

The new gravitational force exerted if the mass of object A is tripled and the distance R is doubled.

Explanation

Let the mass of A be m

Let the mass of B be m'

Thus the gravitational force becomes,

$F=G\frac{m^{\prime}m}{R^2}$

When the mass of A is tripeled we have, m''=3m

The distance between A and B is doubled i.e R'=2R

Thus the new gravitational force is:

$\begin{gathered} F^{\prime}=G\frac{3mm^{\prime}}{\left(2R\right)^2} \\ \Rightarrow F^{\prime}=\frac{3}{4}\frac{Gmm^{\prime}}{R^2} \\ \Rightarrow F^{\prime}=\frac{3}{4}F \end{gathered}$

Conclusion

The new gravitational force is B.3/4F