Question

Consider the equation v = (1/6)zxt2. the dimensions of the variables v, x, and t are [l/t], [l], and [t] respectively. the numerical factor 6 is dimensionless. what must be the dimensions of the variable z, such that both sides of the equation have the same dimensions?

Answer 1

The dimension of the variable
`z` will be:
`[(1)/(t^3)]`

Explanation:

Given equation is:
`v= ((1)/(6))zxt^2`

The dimensions of the variables
`v, x` and
`t` are
`[(l)/(t)], [l]` and
`[t]` respectively.

Replacing all variables by their dimensions, we will get......

`[(l)/(t)]= z[l][t]^2`

`([l])/([t])= z[l][t^2]\\ \\ z= ([l])/([t][l][t^2])=(1)/([t][t^2])=(1)/([t^3])=[(1)/(t^3)]`

So, the dimension of the variable
`z` will be:
`[(1)/(t^3)]`

Answer 2

The dimension of z is
`[(1)/(t^3)]`.

Explanation:

We have been given the dimension of
`v=[(l)/(t)]`,
`x=[l]` and
`t=[t]`

We need to find the dimension of z

Here, l denotes the length and t denotes the time:

We will put the values of the dimension of the variables given to find the dimension of z. and 1/6 is dimensionless.So, neglect it.

`[(l)/(t)]=z\cdot [l]\cdot [t^2]`

Now, we will simplify the above expression so, as to get the value of z

`[(l)/(t\cdot t^2\cdot l)]=z`

`\Rightarrow z=[(1)/(t^3)]`

Hence, the dimension of z is
`[(1)/(t^3)]`