JEE Main 2026 Jan 21 Shift 1, Physics Q7: Units And Dimensions

JEE Main2026Jan 21, Shift 1Physics

Consider a modified Bernoulli equation.

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

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

A
$[M L^{0} T^{- 1}]$ and $[M^{0} L T]$
B
$[M L^{0} T^{- 1}]$ and $[M^{0} L T^{- 1}]$
C
$[M L^{0} T^{- 2}]$ and $[M^{0} L T^{- 2}]$
D
$[M L^{0} T^{- 2}]$ and $[M^{0} L T^{- 1}]$

Solution

Every term in the equation must share the dimensions of pressure $P$ , namely $[M L^{- 1} T^{- 2}]$ .

From $h + B t$ : $B t$ has the dimensions of length $L$ , so $[B] = [L] [T^{- 1}] = [M^{0} L T^{- 1}]$ .

From $A / (B t^{2})$ : this term has the dimensions of pressure, so $[A] = [B] [T^{2}] [M L^{- 1} T^{- 2}] = [L T^{- 1}] [T^{2}] [M L^{- 1} T^{- 2}] = [M L^{0} T^{- 1}]$ .

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JEE Main 2026 Jan 21 Shift 1, Physics Q7: Units And Dimensions

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