Q. The dimensions of $\ \frac{a}{b}$ in the equation $p = \frac{a\ - \ t^{2}}{bx}$ where $p$ is pressure, $x$ is distance and $t$ is time, are
A) $\left\lbrack M^{2}{LT}^{- 3} \right\rbrack$
B) $\left\lbrack {MT}^{- 2} \right\rbrack$
C) $\left\lbrack {LT}^{- 3} \right\rbrack$
D) $\left\lbrack {ML}^{3}T^{- 1} \right\rbrack$
Explanation
Given, $p = \frac{a - t^{2}}{bx}$ or $pbx = a - t^{2}$ By the law of homogeneity of dimensional equation. Dimensions of $a =$ dimensions of $t^{2} = \left\lbrack T^{2} \right\rbrack$ Dimensions of $b =$dimensions of $\frac{t^{2}}{px} = \left\lbrack M^{- 1}T^{4} \right\rbrack$ So, dimensions of $\frac{a}{b}\ is\ \left\lbrack {MT}^{- 2} \right\rbrack$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.