Question

Dimensional formula of $\frac{a}{b}$ satisfying $P=\frac{a - t^{2}}{bx}$ where $P$ is pressure, $x$ is distance and $t$ is time will be

• A. $ML^{1}T^{- 1}$
• B. $M^{2}LT^{- 1}$
• C. $ML^{0}T^{- 2}$
• D. $M^{0}L^{- 1}$

Answer 1

Answer: (C)

$P=\frac{a - t^{2}}{b x}=\frac{a}{b x}-\frac{t^{2}}{b x}$
By the principle of homogeneity.
$\left[\right.P\left]\right.=\frac{\text{ force }}{\text{ area }}=\frac{a}{b \left[\right. x \left]\right.}$
$\text{M}\text{L}^{- 1}\text{T}^{- 2}=\frac{a}{b}\left[\frac{1}{L}\right]\Rightarrow \frac{a}{b}=\text{M}\text{T}^{- 2}$