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=(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(1)/(r^2) \end{gathered}`

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

`\begin{gathered} F^(\prime)\alpha(M*3m)/(r^2) \\ F^(\prime)\alpha(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(2M*2m)/(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(M*(m)/(3))/(r^2) \\ F^(\prime)\alpha(Mm)/(3r^2) \\ F^(\prime)\alpha(F)/(3) \end{gathered}`

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

`\begin{gathered} F^(\prime)\alpha(Mm)/((2r)^2) \\ F^(\prime)\alpha(Mm)/(r^2)*(1)/(4) \\ F^(\prime)\alpha(F)/(4) \end{gathered}`

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

`\begin{gathered} F^(\prime)\alpha(Mm)/((3r)^2) \\ F^(\prime)\alpha(Mm)/(r^2)*(1)/(9) \\ F^(\prime)\alpha(F)/(9) \end{gathered}`

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

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