# `E_(grav)` and r are related by the equation `E_(grav)` =`(GmM)/r` where all the other quantities in the equation are constant. Which two of the following graphs would be straight lines going...

`E_(grav)` and r are related by the equation `E_(grav)` =`(GmM)/r` where all the other quantities in the equation are constant. Which two of the following graphs would be straight lines going through the origin:

`E_(grav)` against r

r against `(E_(grav))^2`

r against `1/(E_(grav))`

`1/E_(grav)` against `1/r`

`E_(grav)` against `r^2`

`E_(grav)` against `1/r`

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### 1 Answer

The variable `E_(grav)=(GmM)/r` where G,m and M are constants. Let `G*m*M = C` . This gives `E_(grav) = C/r`

The graph of `E_(grav)` against r is equivalent to the graph of `C/r ` against r which is not a straight line

r against `(E_(grav))^2` is equivalent to r against `C^2/r^2` which is not a straight line

r against `1/E_(grav)` is equivalent to r against `r/C` , this is a straight line

`1/E_(grav)` against `1/r` is equivalent to `r/C` against `1/r` which is not a straight line

`E_(grav)` against `r^2` is equivalent to `C/r` against `r^2` which is not a straight line

` E_(grav)` against `1/r` is equivalent to `C/r` against `1/r` which is a straight line.

**The options r against `1/E_(grav)` and `E_(grav)` against `1/r ` represent straight lines passing through the origin.**