Question

The variables x, v, and a have the dimensions of [l], [l]/[t], and [l]/[t]2, respectively. these variables are related by an equation that has the form vn = 2ax, where n is an integer constant (1, 2, 3, etc.) without dimensions. what must be the value of n, so that both sides of the equation have the same dimensions?

Answer 1

The value of n must be 2, so that both sides of the equation have the same dimensions.

Step-by-step explanation

The variables
`x, v` and
`a` have the dimensions of
`[l], ([l])/([t])` and
`([l])/([t]^2)` respectively.

These variables are related by an equation that has the form
`v^n= 2ax`

So, the dimension of the left side ⇒
`(v^n)` ⇒
`(([l])/([t]))^n`

and the dimension of the right side ⇒
`(2ax)` ⇒
`([l])/([t]^2) *[l]= ([l]^2)/([t]^2) = (([l])/([t]))^2`

If both sides of the equation have the same dimensions, so...

`(([l])/([t]))^n = (([l])/([t]))^2\\ \\ So.. n= 2`

So, the value of
`n` must be 2.