In the relation

Discussion Forum : Physics

Question -

In the relation P = `alpha/beta overline(e) (alpha z)/(k theta), ` p is pressure z the distance , k is Boltzmann constant and `theta` is the temperature , the dimensional formula of `beta` will be .

Options:

A . `[M^0 L^2 T^0]`

B . `[ML^2T]`

C . `[ML^0T^-1]`

D . `[ML^2T^-1]`

Answer: Option A

Sol. In Given equation , `(alpha z)/(k theta)` should be dimensinless.

`:.` `alpha = (k theta)/(z)`

`rArr [a] = ([ML^2 T^-2 K^-1 xx K])/([L])` = `[MLT^-2]`

and `P = alpha/beta`

`rArr [beta] = [alpha/p] = ([MLT^-2])/([ML^-1T^-2])`

= `[M^0L^2T^0]`

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