Consider the following modified Bernoulli’s equation: $[ \frac{P}{\rho} + g(h + Bt) + \frac{V^2}{2} + \frac{A}{Bt} = \text{constant} ]$ If t has the dimensions of time, then the dimensions of A and B respectively are

Options:

1. $([ML^0T^{-1}]) and ([LT])$
2. $([ML^0T^{-1}]) and ([LT^{-1}])$
3. $([ML^0T^{-2}]) and ([LT^{-2}])$
4. $([ML^0T^{-2}]) and ([LT^{-1}])$

Solution:

All terms must have same dimensions as $( \frac{P}{\rho} )$ → $( L^2T^{-2} )$ From ( h = Bt ): $[ [B] = LT^{-1} ]$ From term $( \frac{A}{Bt} )$: $[ [A] = ML^0T^{-1} ]$ ✅ Correct Answer: (2)