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}}] $