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

Options

A. `PV^(2)T^(2)`
B. `P^(-1)V^(2)T^(2)`
C. `PVT^(2)`
D. `P^(-1)VT^(2)`

Answer

a

Explanation

Let `F prop P^(x)V^(y)T^(z)`
by substituting the following dimensions:
`[P] = [ML^(-1)T^(2)], [V] = [LT^(-1)] , [T] = [T]`
and comparring the dimension of both sides
`x = 1, y = 2, z= 2`, so `F = PV^(2)T^(2)`.