Question:
The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then the potential of each single drop was
The potential of a large liquid drop when eight liquid drops are combined is 20 V. Then the potential of each single drop was
Updated On: Apr 15, 2024
- 10V
- 7.5V
- 5V
- 2.5V
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The Correct Option is C
Solution and Explanation
Volume of 8 small drops = Volume of big drop
$\therefore\left(\frac{4}{3}\pi r^{3}\right) \times8 = \frac{4}{3}\pi R^{3}$
$ \Rightarrow 2r =R$ ....(i)
According to charge conservation
$8q = Q$ ....(ii)
Potential of one small drop $ \left(V'\right) = \frac{q}{4\pi\varepsilon_{0}r}$
Similarly, potential of big drop $ \left(V\right)= \frac{Q}{4\pi\varepsilon_{0}R}$
Now, $ \frac{V'}{V} = \frac{q}{Q}\times\frac{R}{r} $
$\Rightarrow \frac{V'}{20} = \frac{9}{8q}\times\frac{2r}{r}$
[from Eqs. (i) and (ii)]
$ \therefore V' = 5\,V $
$\therefore\left(\frac{4}{3}\pi r^{3}\right) \times8 = \frac{4}{3}\pi R^{3}$
$ \Rightarrow 2r =R$ ....(i)
According to charge conservation
$8q = Q$ ....(ii)
Potential of one small drop $ \left(V'\right) = \frac{q}{4\pi\varepsilon_{0}r}$
Similarly, potential of big drop $ \left(V\right)= \frac{Q}{4\pi\varepsilon_{0}R}$
Now, $ \frac{V'}{V} = \frac{q}{Q}\times\frac{R}{r} $
$\Rightarrow \frac{V'}{20} = \frac{9}{8q}\times\frac{2r}{r}$
[from Eqs. (i) and (ii)]
$ \therefore V' = 5\,V $
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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.