JEE Main 2026 — Physics Mechanics

2026mcqmedium

Consider a modified Bernoulli equation.

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

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

Official previous-year question

Held on 21 Jan 2026 · Verified 6 Jul 2026.

Options

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

Did you get this right?

Solution

All terms must have dimension of pressure $[ML^{-1}T^{-2}]$ .

For $(h + Bt)$ : Since $\rho gh$ has dimension of pressure, $[h] = [L]$ .

For dimensional consistency: $[Bt] = [L]$ , so $[B] = [LT^{-1}] = [M^0LT^{-1}]$

For $\frac{A}{Bt^2}$ : $\frac{[A]}{[B][T^2]} = [ML^{-1}T^{-2}]$

$[A] = [B][T^2][ML^{-1}T^{-2}] = [LT^{-1}][T^2][ML^{-1}T^{-2}] = [ML^0T^{-1}]$

$[A] = [ML^0T^{-1}]$ and $[B] = [M^0LT^{-1}]$

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Options

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

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

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

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

Solution

All terms must have dimension of pressure $[ML^{-1}T^{-2}]$ .

For $(h + Bt)$ : Since $\rho gh$ has dimension of pressure, $[h] = [L]$ .

For dimensional consistency: $[Bt] = [L]$ , so $[B] = [LT^{-1}] = [M^0LT^{-1}]$

For $\frac{A}{Bt^2}$ : $\frac{[A]}{[B][T^2]} = [ML^{-1}T^{-2}]$

$[A] = [B][T^2][ML^{-1}T^{-2}] = [LT^{-1}][T^2][ML^{-1}T^{-2}] = [ML^0T^{-1}]$

$[A] = [ML^0T^{-1}]$ and $[B] = [M^0LT^{-1}]$

JEE Main 2026 — Physics Mechanics

Options

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Solution

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JEE Main Mechanics in other years

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JEE Main 2026 — Physics Mechanics

Options

Did you get this right?

Solution

Your note

JEE Main Mechanics in other years

More JEE Main Mechanics questions

Other Physics topics for JEE Main

Electromagnetism

Modern Physics

Optics

Thermodynamics

Waves & Oscillations

Keep practicing Mechanics