A capillary tube of radius r is dipped inside a large vessel of water. The mass of water raised above water level is M. If the radius of capillary is doubled, the mass of water inside capillary will be
- 5M
- 2M
\(\frac M4\)
- M
The Correct Option is B
Solution and Explanation
Mass of water in capillary rise \(= Ahρ\)
Where,
\(A\) = area of cross-section,
\(h\) = height,
\(ρ\) = density
\(⇒ m = (\pi r^2 )hρ \)
\(⇒ m = (\pi r^2 ).\frac {2σ\ cos \theta}{rρg}\)
\(⇒m∝r\)
If radious is doubled then mass will also get doubled.
\(⇒m’ =2M\)
So, the correct option is (B): 2M
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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.