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Properties of Matter question

2015 · Q143
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Properties of Matter question

2015 · Q143

NEETPhysicsProperties of MatterMCQ+4 / −1
The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of the liquid in the tube is V, the speed of the ejection of the liquid through the holes is
  1. A
    VR2n3r2{{VR{}^2} \over {{n^3}{r^2}}}n3r2VR2​
  2. B
    V2Rnr{{{V^2}R} \over {nr}}nrV2R​
  3. C
    VR2n2r2{{V{R^2}} \over {{n^2}{r^2}}}n2r2VR2​
  4. D
    VR2nr2{{V{R^2}} \over {n{r^2}}}nr2VR2​
View written solutionFree

Correct answer: D

Let the speed of the ejection of the liquid through the holes be v. Then according to the equation of continuity,

πR2V=nπr2v\pi {R^2}V = n\pi {r^2}vπR2V=nπr2v

⇒v=πR2Vnπr2=VR2nr2 \Rightarrow v = {{\pi {R^2}V} \over {n\pi {r^2}}} = {{V{R^2}} \over {n{r^2}}}⇒v=nπr2πR2V​=nr2VR2​

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