Question

Write the dimensions of $a/b$ in the relation $P=\frac{a-t^2}{bx}$; where $P$ is the pressure, $x$ is the distance, and $t$ is the time.

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

Answer 1

Answer: (B)

$M{L}^0{T}^{-2}$

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

$P=\left[{ML}^{-1}{T}^{-2}\right]$

$a$ will have same unit as $t^2$. So, $a=\left[T^2\right]$

$b=\left[\frac{a-t^2}{px}\right]=\frac{\left[T^2\right]}{\left[{ML}^{-1}{T}^{-2}L\right]}=\left[M^{-1}{L}^0{T}^4\right]$

$\frac{a}{b}=\frac{\left[T^2\right]}{\left[M^{-1}{L}^0{T}^4\right]}=\left[{ML}^0{T}^{-2}\right]$