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A uniform capillary tube of inner radius $r$ is dipped vertically into a beaker filled with water. The water rises to a height $h$ in the capillary tube above the water surface in the beaker. The surface tension of water is $σ$ . The angle of contact between water and the wall of the capillary tube is $θ$ . Ignore the mass of water in the meniscus. Which of the following statements is (are) true?

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Answer:

A, C

Solution:

$\frac{2 σ}{R} = ρ g h$ $[R \to R a d i u s o f m e n i s c u s]$
$h = \frac{2 σ}{R ρ g}$ $R = \frac{r}{\cos θ}$ [r→radius of capillary; $θ \to$ contact angle]
$h = \frac{2 σ \cos θ}{r ρ g}$
$(A)$ For given material, $θ = c o n s t a n t$
$h \propto \frac{1}{r}$
$(B)$ h depends on $σ$
$(C)$ If lift is going up with constant acceleration,
$g_{e f f} = (g + a)$
$h = \frac{2 σ \cos θ}{r ρ (g + a)}$ It means h decreases
$(D)$ h is proportional to $\cos θ, N o t θ$

Stream:JEE_ADVSubject:PhysicsTopic:FluidSubtopic:Surface Tension

⏱ 2mℹ️ Source: PYQ_2018

Physics - Fluid Question with Solution | TestHub

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