Question

According to Bernoulli’s theorem, $\frac{p}{d}+\frac{v^2}{2}+gh=$ Constant. The dimensional formula of the constant is:

($P$ is pressure, $d$ is density, $h$ is height, $v$ is velocity and $g$ is accelaration due to gravity)

• A. $M^0{L}^0{T}^0$
• B. $M^0{LT}^0$
• C. $M^0{L}^2{T}^{-2}$
• D. $M^0{L}^2{T}^{-4}$

Answer 1

Answer: (C)

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

Bernouli's theorem gives $\frac{P}{d}+\frac{v^2}{2}+gh=constant$

$\frac{P}{d}$ , $\frac{v^2}{2}$ and $gh$ will have same dimension as the total will have same dimension.

Dimensions of $P/d$ is $\left[M{L}^{-1}{T}^{-2}\right]/\left[M{L}^{-3}{T}^0\right]=\left[M^0{L}^2{T}^{-2}\right]$