Q69 / 75 · JEE Main 2026 (21 January Shift 1) · Physics
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.
$\left(\mathrm{P}+\frac{A}{B t^{2}}\right)+\rho g(h+B t)+\frac{1}{2} \rho V^{2}=$ constant
If $t$ has the dimension of time then the dimensions of $A$ and $B$ are $\_\_\_\_$, $\_\_\_\_$ respectively.
- 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 $\left[\mathrm{M}^{0} \mathrm{LT}\right]$
- Correct answerD$\left[\mathrm{ML}^{0} \mathrm{~T}^{-1}\right]$ 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 $[B] = [M^0LT^{-1}]$
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 $[B] = [M^0LT^{-1}]$
Hence, the correct answer is option: 'D'.