Question

The dimension of $\frac{a}{b}$ in the equation $p=\frac{a-t^2}{bx}$ where p is pressure, x is distance and t is time is

• A. $\left[L{T}^{-3}\right]$
• B. $\left[M{L}^3{T}^{-1}\right]$
• C. $\left[M^{2}L{T}^{-3}\right]$
• D. $\left[M{T}^{-2}\right]$

Answer 1

The correct option is D $\left[M{T}^{-2}\right]$

Given equation $P=\frac{a-t^2}{bx}=\frac{a}{bx}-\frac{t^2}{bx}$

Applying the principal of homogeneity, we have

$\left[pressure\right]=\left[\frac{force}{area}\right]=\left[\frac{a}{bx}\right]$

or $\left[M{L}^{-1}{T}^{-2}\right]=\left[\frac{a}{b}\right]\left[\frac{1}{L}\right]$

or $\left[\frac{a}{b}\right]=\left[M{T}^{-2}\right]$