Question

If $y$ represents the pressure and $x$ represents the position then dimensional expression of $\int \frac{dx}{\sqrt{p^2-y^2}}$

• A. $\left[M{L}^2{T}^{-2}\right]$
• B. $\left[M^{-1}{L}^2{T}^2\right]$
• C. $\left[M^{-1}{L}^2{T}^{-2}\right]$
• D. $\left[M{L}^2{T}^2\right]$

Answer 1

Answer: (B)

$\left[M^{-1}{L}^2{T}^2\right]$

Dimension of pressure = $M{L}^{-1}{T}^{-2}$

Dimensions of p and y has to be equal

Dimensions of $dx=L^1$

$\therefore$ Dimensions of $\int \frac{dx}{\sqrt{p^2-y^2}}$

Dimension of $\frac{dx}{y}=\frac{L^1}{M{L}^{-1}{T}^{-2}}$

$=M^{-1}{L}^2{T}^2$