Consider a modified Bernoulli equation. ( P + (A / Bt^2) ) + rho g(h + Bt) + (1 / 2)rho V^2 = constant If t has the dimension of time then the dimensions of A and B are ______, ______ respectively.

=> [P] = [ (A / Bt^2) ] s (1) => [h] = [Bt] s (2) => [B] = [ (h / t) ] = [ (L / T) ] = [LT^-1] Putting B in equation (1) [ML^-1T^-2] = [ fracALT^-1 x T^2 ] [A] = [ML^0T^-1]

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Consider a modified Bernoulli equation P fracABt 2 rho ... | null (Physics) | DivineJEE

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Physics

JEE Mains 2026 21st January Shift 1

Physics

Consider a modified Bernoulli equation.

\left( P + \frac{A}{Bt^2} \right) + \rho g(h + Bt) + \frac{1}{2}\rho V^2 = \text{constant}

t

has the dimension of time then the dimensions of

A

and

B

are ______, ______ respectively.

[ML^0T^{-1}]

and

[M^0LT]

[ML^0T^{-1}]

and

[M^0LT^{-1}]

[ML^0T^{-2}]

and

[M^0LT^{-2}]

[ML^0T^{-2}]

and

[M^0LT^{-1}]

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Explanation

\Rightarrow [P] = \left[ \frac{A}{Bt^2} \right] \dots (1)

\Rightarrow [h] = [Bt] \dots (2)

\Rightarrow [B] = \left[ \frac{h}{t} \right] = \left[ \frac{L}{T} \right] = [LT^{-1}]

Putting

B

in equation (1)

[ML^{-1}T^{-2}] = \left[ \frac{A}{LT^{-1} \times T^2} \right]

[A] = [ML^0T^{-1}]

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