Physics Exam Questions with Algebra

[Underdogg]

Hey everyone,

 

It seems to be a recurring problem for me, but whenever I'm presented with a question that involves "doubling the value or halving the value" of a variable in an equation, I can never get it right.

In case I haven't made it clear enough, say you had the formula for Newton's Law of Gravitation:

 

F = -GMm/r²

A typical question would be: What would be the new value of the result (from a previous question), if the value of "r" was quartered?

 

Any help is greatly appreciated.

Thank you

[ajb]

I will get you started on your question

 

Let [math]r \longrightarrow \frac{r}{4}[/math], then [math]\frac{1}{r^{2}} \longrightarrow \frac{1}{(\frac{r}{4})^{2}}[/math]. After a little algebra we get

 

[math]\frac{1}{(\frac{r}{4})^{2}} =\left(\frac{4}{r}\right)^{2} [/math]

 

Can you now see what is going on?