Question

For each of the following questions, solve for the unknown quantity by rearranging the given equation.

For numerical answers, make sure to express all answers in scientific notation with the proper number of
significant figures. Be careful to write out all units and convert if necessary.
3.
F=GMm/r^2

a. M =
b. r =
M=kxa^3/p^2

a. P =
b. a =

Answer 1

For F=GMm/r^2

`F = (GMm)/(r^(2) )`

a.
`M = (Fr^(2) )/(Gm)`

b.
`r = \sqrt{(GMm)/(F)}`

M=kxa^3/p^2

`M = (kxa^(3) )/(p^(2) )`

a.
`p = \sqrt{(kxa^(3) )/(M)}`

b.
`a = \sqrt[3]{(Mp^(2) )/(kx)}`

Explanation:

To solve for the unknown quantity, we will make the unknown quantity the subject of the given equation.

For F=GMm/r^2

a. M =

F=GMm/r^2

`F = (GMm)/(r^(2) )`

The first thing to do is cross multiply, so that the equation gives

`Fr^(2) = GMm`

Now, divide both sides of the equation by
`Gm`, we then get

`(Fr^(2) )/(Gm) = (GMm)/(Gm)`

Then,
`(Fr^(2) )/(Gm) = M`

Hence,

`M = (Fr^(2) )/(Gm)`

b. r =

F=GMm/r^2

`F = (GMm)/(r^(2) )`

Likewise, we will first cross multiply, we then get

`Fr^(2) = GMm`

Now, divide both sides by
`F`, so that the equation becomes

`(Fr^(2) )/(F) = (GMm)/(F) \\`

∴
`r^(2) = (GMm)/(F) \\`

Then,

`r = \sqrt{(GMm)/(F)}`

For M=kxa^3/p^2

a. P =

M=kxa^3/p^2

`M = (kxa^(3) )/(p^(2) )`

The first thing to do is cross multiply, so that the equation becomes

`Mp^(2) = kxa^(3) \\`

Now, divide both sides by M, we then get

`(Mp^(2) )/(M) = (kxa^(3) )/(M)`

∴
`p^(2) = (kxa^(3) )/(M)`

Then,

`p = \sqrt{(kxa^(3) )/(M)}`

b. a =

M=kxa^3/p^2

`M = (kxa^(3) )/(p^(2) )`

Also, we will first cross multiply to get

`Mp^(2) = kxa^(3) \\`

Then, divide both sides of the equation by
`kx` to get

`(Mp^(2) )/(kx)= (kxa^(3) )/(kx)\\`

`(Mp^(2) )/(kx)= a^(3)`

∴
`a^(3) = (Mp^(2) )/(kx)`

Then,

`a = \sqrt[3]{(Mp^(2) )/(kx)}`