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Standard XII

Physics

Dimensional Analysis

The given fig...

Question

The given figure shows difference in water level 'h' of communicating capillary tubes of different radii. Radius at A and B are 1 mm and 1.5 mm respectively. Surface tension of water = 0.07 N $m^{- 1}$ and angle of contact between the glass and the water is $0^{0}$ . The value of h (in mm) is (Take g = 9.8 m $s^{- 2}$ )

3.78

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4.76

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5.32

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Solution

The correct option is B 4.76
As, $ρ g h = 2 T (\frac{1}{r_{1}} - \frac{1}{r_{2}})$
Here, $ρ = 10^{3} k g m^{- 3}, g = 9.8 m s^{- 2},$
$T = 0.07 N m^{- 1}, r_{1} = 1 m m, r_{2} = 1.5 m m,$
$∴= \frac{2 T}{ρ g} (\frac{1}{r_{1}} - \frac{1}{r_{2}}) = \frac{2 (0.07)}{10^{3} \times 9.8} (\frac{1}{1 \times 10^{- 3}} - \frac{1}{1.5 \times 10^{- 3}})$
$= 4.76 \times 10^{- 3} m = 4.76 m m$

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Similar questions

Q. The given figure shows difference in water level

h

of two communicating capillary tubes of different diameters

1 m m

and

1.5 m m

respectively. Surface tension of water

= 0.07 N / m

, and angle of contact between the glass and the water is

0^{\circ}

. The value of

h

(in mm) is

(g = 9.8 m / s^{2})

Q. Calculate the difference

(h)

in water level in two communicating capillary tubes of radius

1 m m

and

1.5 m m

. Surface tension of water

= 0.07 N m^{- 1}

A cylindrical capillary tube of $0.2 m m$ radius is made by joining two capillaries $T_{1}$ and $T_{2}$ of different materials having water contact angles of $0^{o}$ and $60^{o}$ respectively. The capillary tube is dipped vertically in water in two different configurations, case I and II as shown in figure . Which of the following option(s) is (are) correct?
[Surface tension of water = $0.075 N / m$ , density of water = $1000 k g / m^{3}$ , take $g = 10 m / s^{2}$ ]

The lower end of a capillary tube is dipped into water and it is seen that the water rises through 7.5 cm in the capillary. Find the radius of the capillary. Surface tension of water = 7.5 × 10^-2 N m^-1. Contact angle between water and glass = 0°. Take g = 10 m s^-2.

Q. Two different vertical positions (a) and (b) of a capillary tube are shown in the figure with the lower end inside water. For position (a) Contact angle is

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and water rises to height h above the surface of water, while for position (b) height of the tube outside water is kept insufficient and equal to

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. Then contact angle becomes:

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The correct option is B 4.76As, ρgh=2T(1r1−1r2) Here,ρ=103kg m−3,g=9.8ms−2, T=0.07Nm−1,r1=1mm,r2=1.5mm, ∴=2Tρg(1r1−1r2)=2(0.07)103×9.8(11×10−3−11.5×10−3) =4.76×10−3m=4.76mm