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Standard XII

Physics

Tube of Insufficient Length

The lower end...

Question

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.

2 mm

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0.2 mm

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0.4 mm

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2 × 10^-3 m

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Solution

The correct option is B
0.2 mm

We have, $h = \frac{2 S c o s θ}{r ρ g}$
or, $r = \frac{2 S c o s θ}{r ρ h}$
= $\frac{2 \times (7.5 \times 10^{- 2} N m^{- 1} \times) 1}{(0.075 m) \times (1000 k g m^{- 3}) \times (10 m s^{- 2})}$
$2 \times 10^{- 4} m = 0.2 m m$

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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.

The correct option is B 0.2 mm We have, h=2Scosθrρg or, r=2Scosθrρh =2×(7.5×10−2Nm−1×)1(0.075m)×(1000kgm−3)×(10ms−2) 2×10−4m=0.2mm

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.

The correct option is B
0.2 mm

We have, $h = \frac{2 S c o s θ}{r ρ g}$
or, $r = \frac{2 S c o s θ}{r ρ h}$
= $\frac{2 \times (7.5 \times 10^{- 2} N m^{- 1} \times) 1}{(0.075 m) \times (1000 k g m^{- 3}) \times (10 m s^{- 2})}$
$2 \times 10^{- 4} m = 0.2 m m$