A certain number of spherical drops of a liquid of radius ‘r’ coalesce to form a single drop of radius ‘R’ and volume ‘V’. If ‘T’ is the surface tensi - Physics MCQ Physics | ExamTest.live | ExamTest.live

Home Tests Search Rank Profile

mediumMCQPhysicsPhysics

1 mark

A certain number of spherical drops of a liquid of radius ‘r’ coalesce to form a single drop of radius ‘R’ and volume ‘V’. If ‘T’ is the surface tension of the liquid, then:

A $energy = 4 V T (\frac{1}{r} - \frac{1}{R}) is released$
B $energy = 3 V T (\frac{1}{r} + \frac{1}{R}) is absorbed$
C $energy = 3 V T (\frac{1}{r} - \frac{1}{R}) is released$
D $energy is neither released nor absorbed$

Solution & Step-by-step Explanation

When n drops of radius r coalesce into one drop of radius R :Volume remains constant: n \times \frac{4}{3} π r^{3} = \frac{4}{3} π R^{3} ⟹ n = \frac{R ^{3}}{r ^{3}} .Change in Surface Area Δ A = 4 π R^{2} - n (4 π r^{2}) . Δ A = 4 π R^{2} - (\frac{R ^{3}}{r ^{3}}) 4 π r^{2} = 4 π R^{2} - 4 π \frac{R ^{3}}{r} = 4 π R^{3} (\frac{1}{R} - \frac{1}{r}) .Energy change Δ U = T Δ A = T \times 4 π R^{3} (\frac{1}{R} - \frac{1}{r}) .Since V = \frac{4}{3} π R^{3}, we have 4 π R^{3} = 3 V . Δ U = 3 V T (\frac{1}{R} - \frac{1}{r}) = - 3 V T (\frac{1}{r} - \frac{1}{R}) .Negative sign indicates energy is released. Magnitude is 3 V T (\frac{1}{r} - \frac{1}{R}) .

Practice this question

Try it yourself before checking the explanation above.

A certain number of spherical drops of a liquid of radius ‘r’ coalesce to form a single drop of radius ‘R’ and volume ‘V’. If ‘T’ is the surface tension of the liquid, then:

A

energy = 4 V T (\frac{1}{r} - \frac{1}{R}) is released

B

energy = 3 V T (\frac{1}{r} + \frac{1}{R}) is absorbed

C

energy = 3 V T (\frac{1}{r} - \frac{1}{R}) is released

D

energy is neither released nor absorbed

Share This Question

Surface Tension Work and Energy

Related Questions

Consider a water tank as shown in the figure. It has one wall at x = L and is very wide in the z direction. When filled with a liquid of surface tension S and density ρ , the liquid surface makes an angle θ_0 ( θ_0 1 ) with the x -axis at x = L . If y(x) is the height of the surface, then the equation for y(x) is:(Take θ(x) ≈ θ(x) ≈ θ(x) = dy/dx and g as acceleration due to gravity) ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/e48999a7-2b29-4d5c-be16-ae2fd5fbcea5.png)

A microscope has an objective of focal length 2 cm , eyepiece of focal length 4 cm and the tube length of 40 cm . If the distance of distinct vision of eye is 25 cm , the magnification in the microscope is:

An electron (mass 9 × 10^-31 kg and charge 1.6 × 10^-19 C ) moving with speed c/100 ( c = speed of light) is injected into a magnetic field B of magnitude 9 × 10^-4 T perpendicular to its direction of motion. We wish to apply a uniform electric field E together with the magnetic field so that the electron does not deflect from its path. Then (speed of light c = 3 × 10^8 ms^-1 ):

There are two inclined surfaces of equal length ( L ) and same angle of inclination 45^ with the horizontal. One of them is rough and the other is perfectly smooth. A given body takes 2 times as much time to slide down on rough surface than on the smooth surface. The coefficient of kinetic friction ( μ_k ) between the object and the rough surface is close to:

The kinetic energies of two similar cars A and B are 100 J and 225 J respectively. On applying breaks, car A stops after 1000 m and car B stops after 1500 m . If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the ratio F_A/F_B is:

The current passing through the battery in the given circuit is: ![image](https://pub-7faa453bd1ec4bf0a04cc031c6f058de.r2.dev/images/5a163a0c-22d0-4a96-bcd2-b569518db0a4.png)

Ready for a Full Test?

Practice with timed mock tests and track your performance across Physics.

Browse Tests Leaderboard

Discussion