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JEE Advanced 2007Paper 2
Exam
JEE Advanced
Year
2007
Paper
Paper 2
Subject
Physics
Chapter
Mechanical Properties of Fluids

JEE Advanced 2007 · Paper 2 · Physics · Mechanical Properties of Fluids

Water is filled up to a height h in a beaker of radius R as shown...

Water is filled up to a height hh in a beaker of radius RR as shown in the figure. The density of water is ρ\rho, the surface tension of water is TT and the atmospheric pressure is p0p_0. Consider a vertical section ABCDA B C D of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude. Water is filled up to a height h in a beaker of radius R as shown in the figure. The density of water is , the surface

Options

  1. A∣2p0Rh+πR2ρgh−2RT∣\left|2 p_0 R h+\pi R^2 \rho g h-2 R T\right|
  2. B∣2p0Rh+Rρgh2−2RT∣\left|2 p_0 R h+R \rho g h^2-2 R T\right|
  3. C∣p0πR2+Rρgh2−2RT∣\left|p_0 \pi R^2+R \rho g h^2-2 R T\right|
  4. D∣p0πR2+Rρgh2+2RT∣\left|p_0 \pi R^2+R \rho g h^2+2 R T\right|

Correct answer

B. ∣2p0Rh+Rρgh2−2RT∣\left|2 p_0 R h+R \rho g h^2-2 R T\right|

Step-by-step solution

Force from right hand side liquid on left hand side liquid. (i) Due to surface tension force =2RT=2 R T(towards ) (ii) Due to liquidpressureforceliquid pressure force=∫x=0x=h(p0+ρgh)(2R\cdotx)dx=(2p0Rh+Rρgh2) (towards left) \begin{aligned}& =\int_{x=0}^{x=h}\left(p_0+\rho g h\right)(2 R \cdotx) d x \\ & =\left(2 p_0 R h+R \rho g h²\right)\text{ (towards left) } \end{aligned}∴\therefore Net force is \left|2 p_0 R h+R \rho g h^2-2 R T\right|$ Correct option is (b).
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