Water is being filled at the rate of 1 cm3/sec in a right circular conical vessel (vertex downwards) of height 35 cm and diameter 14 cm. When the height of the water level is 10 cm, the rate (in cm2/sec) at which the wet conical surface area of the vessel increase, is
- 5
- \(\frac{\sqrt21}{5}\)
- \(\frac{\sqrt26}{5}\)
- \(\frac{\sqrt26}{10}\)
The Correct Option is A
Solution and Explanation
The correct option is(C): \(\frac{\sqrt26}{5}\).
\(s=\pi{l}=\pi(\frac{h}{5}\sqrt{h^2+\frac{h^2}{25}}=\frac{\pi}{25}\sqrt{26h^2})\)
\(⇒\frac{ds}{dt}(h=10)=\frac{\sqrt26}{5}\)
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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.