Question

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

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

Answer 1

Answer: (D)

$\left[P^1{V}^2{T}^2\right]$

$Force=P^x{V}^y{T}^z$

$\left[ML{T}^{-2}\right]=\left[ML{T}^{-2}{L}^{-2}{]}^x\right[L{T}^{-1}{]}^y[T{]}^z$

Comparing the dimensions on both side, we get,

$x=1$, $y=2$, $z=2$

So, $Force=\left[P^1{V}^2{T}^2\right]$