Question

If pressure $P$, velocity $V$ and the time $T$ are taken as fundamental physical quantities, the dimensional formula of the force is:

• A. $P{V}^2{T}^2$
• B. $P^{-1}{V}^2{T}^{-2}$
• C. $PV{T}^2$
• D. $P^{-1}V{T}^2$

Answer 1

The correct option is A $P{V}^2{T}^2$

$F=P^{\alpha }{v}^{\beta }{T}^{\gamma }$
or, $\left[M^1{L}^1{T}^{-2}\right]=\left[M^{\alpha }{L}^{-\alpha +\beta }{T}^{-2\alpha -\beta +\gamma }\right]$
i.e. $\left[M^1{L}^1{T}^{-2}\right]=\left[M^{\alpha }{L}^{-\alpha +\beta }{T}^{-2\alpha -\beta +\gamma }\right]$
Hence we have,
$\alpha =1$, $-\alpha +\beta =1$ and $-2\alpha -\beta +\gamma =-2$
Solving these we get,
$\alpha =1$, $\beta =2$, $\gamma =2$
$\Rightarrow F=P{v}^2{T}^2$