JEE Advanced · Physics · 11. Properties of Fluids

Paragraph :
A spray gun is shown in the figure where a piston pushes air out of a nozzle. A thin tube of uniform cross section is connected to the nozzle. The other end of the tube is in a small liquid container. As the piston pushes air through the nozzle, the liquid from the container rises into the nozzle and is sprayed out. For the spray gun shown, the radii of the piston and the nozzle are $20 \mathrm{~mm}$ and $1 \mathrm{~mm}$, respectively. The upper end of the container is open to the atmosphere.

Question :
If the piston is pushed at a speed of $5 \mathrm{~mms}^{-1}$, the air comes out of the nozzle with a speed of

A $0.1 m s^{- 1}$
B $1 m s^{- 1}$
C $2 m s^{- 1}$
D $8 m s^{- 1}$

Verified Solution

Answer & Solution

Correct Answer

(C) $2 m s^{- 1}$

Step-by-step Solution

Detailed explanation

A_{1} V_{1} = A_{2} V_{2}

\Rightarrow π {(20)}^{2} \times 5 = π {(1)}^{2} V_{2} \Rightarrow V_{2} = 2 \frac{m}{s^{2}}

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.

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