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. $[LT^{-3}]$
• B. $[ML^3T^{-1}]$
• C. $[M^2LT^{-3}]$
• D. $[MT^{-2}]$

Answer 1

Answer: (D)

Given equation $P=\frac{a-t^{2}}{b x}=\frac{a}{b x}-\frac{t^{2}}{b x}$
Applying the principal of homogeneity, we have
[pressure] $=\left[\frac{\text { force }}{\text { area }}\right]=\left[\frac{a}{b x}\right] $
or $\left[ ML ^{-1} T ^{-2}\right] =\left[\frac{a}{b}\right]\left[\frac{1}{L}\right]$
or $\left[\frac{a}{b}\right]=\left[ MT ^{-2}\right]$