Q: The dimensional formula of a/b in the Equation $ P = \frac{a-ct^2}{bx} $ , where P = pressure, x = displacement and t = time

Sol: $\large [P] = \frac{a}{bx} – \frac{ct^2}{bx}$

By principle of Homogeneity, [a/bx]should represent pressure

$\large \frac{a}{bx} = [\frac{a}{b}]\frac{1}{L} = [M L^{-1}T^{-2}]$

$\large [\frac{a}{b}] = [M T^{-2}]$