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) $MT^{- 2}$
B) $M^{2}LT^{- 3}$
C) $ML^{3}T^{- 1}$
D) $LT^{- 3}$
Explanation
$\lbrack a\rbrack = \lbrack T^{2}\rbrack$ and $\lbrack b\rbrack = \frac{\lbrack a - t^{2}\rbrack}{\lbrack P\rbrack\lbrack X\rbrack} = \frac{T^{2}}{\left\lbrack ML^{- 1}T^{- 2} \right\rbrack\lbrack L\rbrack}$ $\Rightarrow \lbrack b\rbrack = \lbrack M^{- 1}T^{4}\rbrack$ So $\left\lbrack \frac{a}{b} \right\rbrack = \frac{\lbrack T^{2}\rbrack}{\lbrack M^{- 1}T^{4}\rbrack} = \lbrack MT^{- 2}\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.