Question

According to Bernoullis theorem $\frac{P}{d}+\frac{V_2}{2}+gh=cons\tan t.$ The dimensional formula of the constant is: (P = pressure, d = density, h = height, V = velocity and g = acceleration due to gravity)

• A. $\left[M^0{L}^0{T}^0\right]$
• B. $\left[M^{0}L{T}^0\right]$
• C. $\left[M^0{L}^2{T}^{-2}\right]$
• D. $\left[M^0{L}^2{T}^{-4}\right]$

Answer 1

Answer: (C)

According to Bernoullis theorem $\frac{P}{d}+\frac{V^2}{2}+gh=cons\tan t$ Since, only same quantities can be added or subtracted. Therefore, dimensional formula of the constant = Dimensional formula of $\frac{P}{d}$ = Dimensional formula of $V^2/2$ = Dimensional formula of gh $\because$ Dimensional formula of $g=[M^0{L}^1{T}^{-2}]$ Dimensional formula of $h=[M^0{L}^1{T}^0]$ $\because$ Dimensional formula of the constant $=[M^0{L}^1{T}^{-2}][M^0{L}^1{T}^0]=[M^0{L}^2{T}^{-2}]$