Question:
A capillary tube of radius $r$ can support a liquid of weight $6.28 \times 10^{-4} \,N$. If the surface tension of the liquid is $5 \times 10^{-2} \,N / m$. The radius of capillary must be
A capillary tube of radius $r$ can support a liquid of weight $6.28 \times 10^{-4} \,N$. If the surface tension of the liquid is $5 \times 10^{-2} \,N / m$. The radius of capillary must be
Updated On: Jun 23, 2023
- $2.0 \times 10^{-3} m$
- $20 \times 10^{-4} m$
- $1.5 \times 10^{-3} m$
- $12.5 \times 10^{-4} m$
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The Correct Option is A
Solution and Explanation
$W=T . 2 \pi r$
$ r =\frac{W}{2 \pi T}=\frac{6.28 \times 10^{-4}}{2 \times 3.14 \times 5 \times 10^{-2}} $
$=2 \times 10^{-3} m$
$ r =\frac{W}{2 \pi T}=\frac{6.28 \times 10^{-4}}{2 \times 3.14 \times 5 \times 10^{-2}} $
$=2 \times 10^{-3} m$
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Concepts Used:
Surface Tension
The amount of energy required to increase the liquid's surface area by one unit area is known as surface tension. In other words, it is a property of the liquid surface to resist force.
Surface tension is defined as,
The ratio of the surface force F to the length L along which the force acts.
Mathematically, the surface tension formula can be expressed as follows:
T=F/L
Where,
- F is the force per unit length
- L is the length in which force act
- T is the surface tension of the liquid
Read More: Detergents and Surface Tension
Factors affecting surface tension:
- Impurities: The surface tension decreases with the addition of impurities.
- Surfactants: Adding surfactants in liquids lowers the tension of water making it interrupt aside or get susceptible.
- Temperature: The surface tension of a liquid reduces as the temperature rises.
The Unit of Surface Tension:
The SI unit of Surface Tension is Newton per Meter or N/m.