Question

what happens to F 1. m is doubled2. m is tripled3. m an m are both doubled4. m is halved5. r is doubled6. r is tripled7. r is increased 10 times8. r is halved

Answer 1

The expression for the gravitational force is given as:

$F_g=\frac{GMm}{r^2}$

1. When M is doubled, then force will also be doubled as Force is directly proportional to the mass.

$\begin{gathered} F\alpha M \\ F\alpha m \\ F\alpha\frac{1}{r^2} \end{gathered}$

2. When the m is tripled, then force will be tripled.

$\begin{gathered} F^{\prime}\alpha\frac{M\times3m}{r^2} \\ F^{\prime}\alpha\frac{3Mm}{r^2} \\ F^{\prime}\alpha3F \end{gathered}$

3. When both M and m are doubled then, the force will become four times.

$\begin{gathered} F^{\prime}\alpha\frac{2M\times2m}{r^2} \\ F^{\prime}\alpha4F \end{gathered}$

4.When m is halved, then Force will be halved, as force is directly proportional to the mass.

$\begin{gathered} F^{\prime}\alpha\frac{M\times\frac{m}{3}}{r^2} \\ F^{\prime}\alpha\frac{Mm}{3r^2} \\ F^{\prime}\alpha\frac{F}{3} \end{gathered}$

5. When distance is doubled, then force will become one-fouth.

$\begin{gathered} F^{\prime}\alpha\frac{Mm}{(2r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{4} \\ F^{\prime}\alpha\frac{F}{4} \end{gathered}$

6.When the distance is tripled, the force will become one-ninth.

$\begin{gathered} F^{\prime}\alpha\frac{Mm}{(3r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{9} \\ F^{\prime}\alpha\frac{F}{9} \end{gathered}$

7. When the distance is increased to ten times, the force will become one-hundredth.

$\begin{gathered} F^{\prime}\alpha\frac{Mm}{(10r)^2} \\ F^{\prime}\alpha\frac{Mm}{r^2}\times\frac{1}{100} \\ F^{\prime}\alpha\frac{F}{100} \\ 8.\text{ When the distance in halved, the force will be four time.} \\ F^{\prime}\alpha\frac{Mm}{(\frac{r}{2})^2} \\ F^{\prime}\alpha4\frac{Mm}{r^2} \\ F^{\prime}\alpha4F \end{gathered}$