Question

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

• A. $\left[P^{-1}{V}^2{T}^{-2}\right]$
• B. $\left[P{V}^2{T}^2\right]$
• C. $\left[P^{-1}V{T}^2\right]$
• D. $\left[PV{T}^2\right]$

Answer 1

The correct option is B $\left[P{V}^2{T}^2\right]$

According to the question force,
$F\propto P^{\alpha }{V}^{\beta }{T}^{\gamma }$
by substituting the dimensions,
$\left[ML{T}^{-2}\right]={\left[M{L}^{-1}{T}^{-2}\right]}^{\alpha }{\left[L{T}^{-1}\right]}^{\beta }[T{]}^{\gamma }$
Comparing the power on both sides,
$\alpha =1$
$-\alpha +\beta =1$
$-2\alpha -\beta +\gamma =-2$
by solving above equation, we get
$\alpha =1$, $\beta =2$ and $\gamma =2$
so,
$F\propto P{V}^2{T}^2$
$\text{dimensional formula of force}=\left[P{V}^2{T}^2\right]$

Final answer: (a)