Consider a modified Bernoulli equation. \[\left(\mathrm{P}+\frac{\mathrm{A}}{\mathrm{Bt}^{2}}\right)+\rho \mathrm{g}(\mathrm{~h}+\mathrm{Bt})+\frac{1}{2} \rho \mathrm{~V}^{2}=\text { constant }\] If t has the dimension of time then the dimensions of A and B are \_\_\_\_ , \_\_\_\_ respectively.

(B) $\left[\mathrm{ML}^{0} \mathrm{~T}^{-1}\right]$ and $\left[\mathrm{M}^{0} \mathrm{LT}^{-1}\right]$

(A) $\left[\mathrm{ML}^{0} \mathrm{~T}^{-1}\right]$ and $\left[\mathrm{M}^{0} \mathrm{LT}\right]$

(C) $\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]$ and $\left[\mathrm{M}^{0} \mathrm{LT}^{-2}\right]$

(D) $\left[\mathrm{ML}^{0} \mathrm{~T}^{-2}\right]$ and $\left[\mathrm{M}^{0} \mathrm{LT}^{-1}\right]$

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Units & Measurement

Consider a modified Bernoulli equation.

(P + \frac{A}{Bt ^{2}}) + ρ g (h + Bt) + \frac{1}{2} ρ V^{2} = constant

If t has the dimension of time then the dimensions of A and B are ____ , ____ respectively.

Answer: (B)

Every term added in the equation must carry the dimensions of pressure,

[P] = M L^{- 1} T^{- 2}

. In

ρ g (h + B t)

the quantity

B t

must match

h

, a length, so

[B] = L/T = M^{0} L T^{- 1}

. In

\frac{A}{B t ^{2}}

the whole term equals a pressure, so

[A] = [P] [B] [t^{2}] = M L^{- 1} T^{- 2} \cdot L T^{- 1} \cdot T^{2} = M L^{0} T^{- 1}

. Thus

A

has dimensions

M L^{0} T^{- 1}

and

B

has dimensions

M^{0} L T^{- 1}

JEE Main · 2026 · 21 Jan 2026 · Shift 1 · Single correct option