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Properties of Matter question

2014 · Shift 2 · Q56
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Properties of Matter question

2014 · Shift 2 · Q56

JEE AdvancedPhysicsProperties of MatterMCQ+3 / −1
A spray gun is shown in the below 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. JEE Advanced 2014 Paper 2 Offline Physics - Properties of Matter Question 18 English ComprehensionIf the piston is pushed at a speed of 5 mm s −-− 1, the air comes out of the nozzle with a speed of
  1. A
    0.1 ms−10.1 \mathrm{~ms}^{-1}0.1 ms−1
  2. B
    1 ms−11 \mathrm{~ms}^{-1}1 ms−1
  3. C
    2 ms−12 \mathrm{~ms}^{-1}2 ms−1
  4. D
    8 ms−18 \mathrm{~ms}^{-1}8 ms−1
View written solutionFree

Correct answer: C

  1. Use continuity equation for air flow

As the piston pushes air into the nozzle, the volume flow rate must remain the same:

Apvp=AnvnA_p v_p = A_n v_nAp​vp​=An​vn​

where:

  • Ap=πrp2A_p = \pi r_p^2Ap​=πrp2​ = area of piston
  • An=πrn2A_n = \pi r_n^2An​=πrn2​ = area of nozzle
  • vp=5 mm s−1v_p = 5\,\text{mm s}^{-1}vp​=5mm s−1
  • vnv_nvn​ = speed of air at nozzle
  1. Substitute the radii

Given:

  • piston radius rp=20 mmr_p = 20\,\text{mm}rp​=20mm
  • nozzle radius rn=1 mmr_n = 1\,\text{mm}rn​=1mm

So,

vn=ApAnvp=π(20)2π(1)2×5 mm s−1v_n = \frac{A_p}{A_n} v_p = \frac{\pi (20)^2}{\pi (1)^2} \times 5\,\text{mm s}^{-1}vn​=An​Ap​​vp​=π(1)2π(20)2​×5mm s−1

vn=400×5 mm s−1=2000 mm s−1v_n = 400 \times 5\,\text{mm s}^{-1} = 2000\,\text{mm s}^{-1}vn​=400×5mm s−1=2000mm s−1

  1. Convert to SI units

2000 mm s−1=2 m s−12000\,\text{mm s}^{-1} = 2\,\text{m s}^{-1}2000mm s−1=2m s−1

  1. Match with options

Thus the air comes out with speed:

2 m s−1\boxed{2\,\text{m s}^{-1}}2m s−1​

So the correct option is C.

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