JEE Mains · Physics · STD 11 - 9.1 fluid mechanics

A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity \(0.8\)). The height of water is \(3\,m\) and that of kerosene \(2\,m\). When the hole is opened the velocity of fluid coming out from it is nearly ........ \(ms^{-1}\) .(take \(g\, = 10\, m s^{-2}\) and density of water \(= 10^3\, kg\, m^{-3}\))

A \(10.7\)
B \(9.6\)
C \(8.5\)
D \(7.6\)

Verified Solution

Answer & Solution

Correct Answer

(B) \(9.6\)

Step-by-step Solution

Detailed explanation

\({h_1}{\rho _1}g + {h_2}{\rho _2}g = \frac{1}{2}{\rho _1}{v^2}\) \( \Rightarrow 1000 \times 10 \times 3 + 800 \times 10 \times 2\) \( = \frac{1}{2} \times 1000 \times {v^2}\) \( \Rightarrow {v^2} = 2 \times \frac{{46000}}{{1000}}\) \( \Rightarrow v = \sqrt {92} = 9.6\,m/s\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List \(I\) with List \(II\)

LIST \(I\)	LIST \(II\)
\(A\) Planck's constant \(( h )\)	\(I\) \(\left[ M ^1 L ^2 T ^{-2}\right]\)
\(B\) Stopping potential \(( Vs )\)	\(II\) \(\left[ M ^1 L ^1 T ^{-1}\right]\)
\(C\) Work function \((\phi)\)	\(III\) \(\left[ M ^1 L ^2 T ^{-1}\right]\)
\(D\) Momentum \(( p )\)	\(IV\) \(\left[ M ^1 L ^2 T ^{-3} A ^{-1}\right]\)

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