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← JEE Advanced 2014 · Paper 2
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JEE Advanced 2014 · Paper 2, Physics question 13

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Paragraph For Questions 13 & 14

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 mm and 1 mm, respectively. The upper end of the container is open to the atmosphere.

Spray gun: a handle and piston rod push a piston along a wide horizontal cylinder ending in a narrow nozzle; a thin vertical tube from the nozzle dips into an open liquid container below, and a spray emerges from the nozzle.

If the piston is pushed at a speed of 5 mm s−15\ \mathrm{mm\,s^{-1}}, the air comes out of the nozzle with a speed of

Choose one option
Answer and worked solution

Official answer: C

Continuity. A1v1=A2v2A_1v_1=A_2v_2:
v2=v1(r1r2)2=5 mm s−1×(201)2=2000 mm s−1=2 m s−1.v_2=v_1\left(\frac{r_1}{r_2}\right)^2=5\ \mathrm{mm\,s^{-1}}\times\left(\frac{20}{1}\right)^2=2000\ \mathrm{mm\,s^{-1}}=2\ \mathrm{m\,s^{-1}}.

(C)

Topics:Continuity equation
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