Tag: surface tension

Questions Related to surface tension

A spherical water drop of radius $R$ is split up into $8$ equal droplets. If $T$ is the surface tension of water, then the work done in this process is-

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. $4\pi R^2T$

  2. $8\pi R^2T$

  3. $48\pi R^2T$

  4. $2\pi R^2T$

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Correct Option: A
Explanation:

Let smaller drop has radius $r$

Volume will remain same. 
$\dfrac{4}{3}\pi R^3 = 8\times \dfrac{4}{3} \pi r^3  \implies   r= \dfrac{R}{2}$

Change in surface energy-
 $A _2T - A _1T = 8\times 4\pi r^2T-4\pi R^2T=4\pi[2R^2-R^2]T=4\pi R^2T$
Work done  = change in surface energy  = $4\pi R^2T$

A drop of oil is placed on the surface of water. Which of the following statement is correct?

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. It will remain on it as a sphere

  2. It will spread as a thin layer

  3. It will partly be as spherical droplets and partly as thin film

  4. It will float as distorted drop on the water surface.

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Correct Option: B
Explanation:

Adhesive force between oil and water molecules is greater than cohesive force between oil molecules. So the oil molecules do not mix with water molecules. As a result, oil spreads on the water surface forming a thin layer.

One thousand small water droplets of equal size combine to form a big drop. The ratio of the final surface energy to the initial surface energy is: (Surface tension of water = 70 dyne/cm) 

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. 10:1

  2. 1000:1

  3. 1:10

  4. 1:1000

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Correct Option: C
Explanation:

Let the radius of smaller radius be $r$ and bigger be $R$.

Since volume remains constant, thus  $\dfrac{4\pi R^3}{3}=1000\times \dfrac{4\pi r^3}{3}$
We get  $R=10r$
Ratio of final surface energy to initial is 
$\dfrac{W _f}{W _i}=\dfrac{T\times 4\pi R^2}{T\times 1000\times 4\pi r^2}$
$\dfrac{W _f}{W _i}=\dfrac{(10r)^2}{1000r^2}=1:10$

A metal plane having an area of $0.04\ m^{2}$ is placed on a horizontal wooden surface. Oil of coefficient of viscosity $2\ N/ s/m^{2}$ is introduced between the plate and the surface till the thickness of the oil layer is $0.5$ in. The horizontal force needed to drag the plate along the surface with a velocity of $5\ cm/s$ is  

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. $80\ N$

  2. $8\ N$

  3. $60\ N$

  4. $6\ N$

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Correct Option: A

Two spherical soap bubbles of a radii $r _1$ and $r _2$ in vacuum coalesce under isothermal conditions. The resulting bubble has the radius $R$ such that

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. $R=r _1+r _2$

  2. $R^2 ={ r _1^2 + r _2^2}$

  3. $R=\dfrac{r _1+r _2}{r _2}$

  4. none of these

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Correct Option: B

What is the change in surface energy, when a mercury drop of radius $R$ splits up into $1000$ droplets of radius $r$?

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. $8\pi R^2T$

  2. $16\pi R^2T$

  3. $24\pi R^2T$

  4. $36\pi R^2T$

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Correct Option: D
Explanation:

Let Surface Tension be T.

Initial surface = $4\Pi { R }^{ 2 }$
Final Surface area = $1000\times 4\Pi { r }^{ 2 }$
& Initial Volume = final volume
$\dfrac { 4 }{ 3 } \Pi { R }^{ 3 }=1000\times \dfrac { 4 }{ 3 } \Pi { r }^{ 3 }$
R = 10r
So,
    Final surface area = $1000\times 4\Pi \times \dfrac { { R }^{ 2 } }{ 100 } =40\Pi { R }^{ 2 }$
So, Workdone = Change in Surface energy
                         = $T\Delta A=(40-4)\Pi { R }^{ 2 }T$
       $\boxed { Change\quad in\quad Surface\quad energy=36\Pi { r }^{ 2 }T } $.

Potential energy of a molecule on the surface of a liquid is as compared to another molecule inside of the liquid is

surface tension physics surface energy of a liquid work done in stretching a liquid surface: surface energy of a liquid properties of matter

  1. More

  2. Less

  3. Both a and b

  4. None of these

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Correct Option: A
Explanation:

Due to surface Tension, Potential energy of a molecule at free surface is more than the molecules inside the liquid.

Which of the following is associated with liquid only and not for the gases?

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. Pressure

  2. Volume

  3. Density

  4. Surface tension

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Correct Option: D
Explanation:

Surface tension is the energy possessed by the free surface of liquids, and it is concerned with only liquid as gases do not have free surfaces.

The property of fluid which enables it to resist tensile stress is known as 

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. compressibility

  2. surface tension

  3. cohesion

  4. adhesion

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Correct Option: B
Explanation:

Surface tension is the property of a fluid which enables it to resist tensile stress.

Surface tension, $S=\dfrac{F}{l}$
It is measured in Newton.

A wire 10  cm long is placed horizontally on the surface of water. It is gently pulled up with a force of $1.4 \times 10^{-2}$ N to keep it in equilibrium. The surface tension of water is

intermolecular forces: cohesive and adhesive forces surface tension properties of matter physics

  1. 50 dyne /cm

  2. 60 dyne/cm

  3. 70 dyne/cm

  4. 40 dyne/cm

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Correct Option: A