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.

Step-by-step explanation

Let the mass of A be m

Let the mass of B be m'

Thus the gravitational force becomes,

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

Conclusion

The new gravitational force is B.3/4F