Mechanical Properties of Fluids NEET PYQ – Chapter-wise Previous Year Questions & Solutions

Q 1 :
Consider a water tank shown in the figure. It has one wall at $x = L$ and can be taken to be very wide in the $z$ -direction. When filled with a liquid of surface tension $S$ and density $ρ$ , the liquid surface makes 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

[IMAGE 96]

(Take $θ (x) = \sin θ (x) = \tan θ (x) = \frac{d y}{d x},$ $g$ is the acceleration due to gravity) [2025]

$\frac{d^{2} y}{d x^{2}} = \sqrt{\frac{ρ g}{S}}$
$\frac{d y}{d x} = \sqrt{\frac{ρ g}{S}} x$
$\frac{d^{2} y}{d x^{2}} = \frac{ρ g}{S} x$
$\frac{d^{2} y}{d x^{2}} = \frac{ρ g}{S} y$

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(4)

[IMAGE 97]

$P_{A} = P_{B} = P_{O}$

$P_{C} = P_{O} - ρ g y$ ...(i)

$P_{C} = P_{O} - \frac{S}{R}$ ...(ii)

So, $ρ g y = \frac{S}{R}$ ...(iii)

Now, $R = \frac{{1 + {(\frac{d y}{d x})}^{2}}^{3 / 2}}{\frac{d^{2} y}{d x^{2}}}$ (radius of curvature)

As $\frac{d y}{d x}$ is small, so $R = \frac{1}{\frac{d^{2} y}{d x^{2}}}$

Putting in eqn. (iii),

$ρ g y = S \times \frac{d^{2} y}{d x^{2}}$

$\frac{d^{2} y}{d x^{2}} = \frac{ρ g y}{S}$

Q 2 :
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is $0.07$ ${Nm}^{- 1}$ , then the excess force required to take it away from the surface is [2024]

19.8 mN
198 N
1.98 mN
99 N

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(1)

Surface tension of water, $T = 0.07$ $N$ $m^{- 1}$

Radius of disc, $r = 4.5$ cm

Required excess pressure, $P = \frac{2 T}{r}$

$∴$ Required force to take it away from the surface is $F = (P) \times Area$

or $F = \frac{2 T}{r} \times π r^{2} = 2 \times T \times (π r)$

$= 2 \times 0.07 \times 3.14 \times 4.5 \times 10^{- 2} = 1.978 \times 10^{- 2} = 19.8 mN$

Q 3 :
Which of the following statement is not true? [2023]

Coefficient of viscosity is a scalar quantity
Surface tension is a scalar quantity
Pressure is a vector quantity
Relative density is a scalar quantity

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(3)

Pressure is ratio of magnitude of force to the area. Therefore, pressure is a scalar quantity.

Q 4 :
The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = $0.03 N$ $m^{- 1}$ ) [2023]

$3.01 \times 10^{- 4}$ $J$
$50.1 \times 10^{- 4}$ $J$
$30.16 \times 10^{- 4}$ $J$
$5.06 \times 10^{- 4}$ $J$

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(1)

We know that surface tension,

$S = \frac{Surface energy}{Surface area} \Rightarrow S = \frac{U}{A} \Rightarrow U = S A$

$= (0.03) \times 2 \times (4 π r^{2}) = (0.03) \times 2 \times (4 \times 3.14) \times {(2 \times 10^{- 2})}^{2}$

$= 3.014 \times 10^{- 4}$ $J .$

Q 5 :
If a soap bubble expands, the pressure inside the bubble [2022]

decreases
increases
remains the same
is equal to the atmospheric pressure

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(1)

The excess pressure inside a soap bubble is

$P_{i} = \frac{4 T}{R} + P_{o}$

where, $P_{i} \to$ inside pressure, $P_{o} \to$ outside pressure

$T =$ surface tension and $R$ is radius.

Here, $P_{o}, T$ is constant, so when $R$ increases, $P_{i}$ decreases.

So, the pressure inside the bubble decreases.

Q 6 :
A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$ . The mass of the water in the capillary is 5 g. Another capillary tube of radius $2 r$ is immersed in water. The mass of water that will rise in this tube is [2020]

2.5 g
5.0 g
10.0 g
20.0 g

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(3)

Force of surface tension balances the weight of water in capillary tube.

$F_{s} = T \cos θ (2 π r) = m g$

$m \propto r$

Hence, $\frac{m'}{m} = \frac{r'}{r} \Rightarrow \frac{m'}{5 g} = \frac{2 r}{r} \Rightarrow m' = 10$ $g$

Q 7 :
A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5 \times 10^{- 2} N/m$ . The pressure inside the bubble equals that at a point $Z_{0}$ below the free surface of water in a container. Taking $g = 10 {m/s}^{2}$ , density of water $= 10^{3} {kg/m}^{3}$ , the value of $Z_{0}$ is [2019]

0.5 cm
100 cm
10 cm
1 cm

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(4)

The pressure at a point $Z_{0}$ below the surface of water, $P_{Z_{0}} = P_{0} + ρ g Z_{0}$

Also, pressure inside a soap bubble, $P = P_{0} + \frac{4 T}{R}$

As per question, $P_{Z_{0}} = P$ $∴$ $P_{0} + \frac{4 T}{R} = P_{0} + ρ g Z_{0}$

$Z_{0} = \frac{4 T}{R ρ g} = \frac{4 \times 2.5 \times 10^{- 2}}{1 \times 10^{- 3} \times 10^{3} \times 10} = 1 \times 10^{- 2} m = 1$ $cm$

Q 8 :
A rectangular film of liquid is extended from $(4 cm \times 2 cm)$ to $(5 cm \times 4 cm)$ . If the work done is $3 \times 10^{- 4}$ $J$ , the value of the surface tension of the liquid is [2016]

0.250 N $m^{- 1}$
0.125 N $m^{- 1}$
0.2 N $m^{- 1}$
8.0 N $m^{- 1}$

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(2)

Work done = Surface tension of film $\times$ Change in area of the film

or, $W = T \times Δ A$

Here, $A_{1} = 4 cm \times 2 cm = 8 {cm}^{2}, A_{2} = 5 cm \times 4 cm = 20 {cm}^{2}$

$Δ A = 2 (A_{2} - A_{1}) = 24 {cm}^{2} = 24 \times 10^{- 4} m^{2}$

$W = 3 \times 10^{- 4} J, T = ?$

$∴$ $T = \frac{W}{Δ A} = \frac{3 \times 10^{- 4}}{24 \times 10^{- 4}} = \frac{1}{8} = 0.125$ $N$ $m^{- 1}$

Q 9 :
Three liquids of densities $ρ_{1}, ρ_{2}$ and $ρ_{3}$ (with $ρ_{1} > ρ_{2} > ρ_{3}$ ), having the same value of surface tension $T$ , rise to the same height in three identical capillaries. The angles of contact $θ_{1}, θ_{2}$ and $θ_{3}$ obey [2016]

$\frac{π}{2} > θ_{1} > θ_{2} > θ_{3} \geq 0$
$0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2}$
$\frac{π}{2} < θ_{1} < θ_{2} < θ_{3} < π$
$π > θ_{1} > θ_{2} > θ_{3} > \frac{π}{2}$

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(2)

Capillary rise, $h = \frac{2 T \cos θ}{r ρ g}$

For a given value of $T$ and $r,$ $h \propto \frac{\cos θ}{ρ}$

Also, $h_{1} = h_{2} = h_{3}$ or $\frac{\cos θ_{1}}{ρ_{1}} = \frac{\cos θ_{2}}{ρ_{2}} = \frac{\cos θ_{3}}{ρ_{3}}$

Since, $ρ_{1} > ρ_{2} > ρ_{3}$ , so $\cos θ_{1} > \cos θ_{2} > \cos θ_{3}$

For $0 \leq θ < \frac{π}{2},$ $θ_{1} < θ_{2} < θ_{3}$

Hence, $0 \leq θ_{1} < θ_{2} < θ_{3} < \frac{π}{2}$

Q 10 :
Water rises to a height $h$ in capillary tube. If the length of capillary tube above the surface of water is made less than $h$ , then [2015]

water rises up to a point a little below the top and stays there
water does not rise at all
water rises up to the tip of capillary tube and then starts overflowing like a fountain
water rises up to the top of capillary tube and stays there without overflowing.

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(4)

Water will not overflow but will change its radius of curvature.

Topic Question Set

Q 2 :
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is $0.07$ ${Nm}^{- 1}$ , then the excess force required to take it away from the surface is [2024]

Q 3 :
Which of the following statement is not true? [2023]

Q 4 :
The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = $0.03 N$ $m^{- 1}$ ) [2023]

Q 5 :
If a soap bubble expands, the pressure inside the bubble [2022]

Q 6 :
A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$ . The mass of the water in the capillary is 5 g. Another capillary tube of radius $2 r$ is immersed in water. The mass of water that will rise in this tube is [2020]

Q 8 :
A rectangular film of liquid is extended from $(4 cm \times 2 cm)$ to $(5 cm \times 4 cm)$ . If the work done is $3 \times 10^{- 4}$ $J$ , the value of the surface tension of the liquid is [2016]

Q 9 :
Three liquids of densities $ρ_{1}, ρ_{2}$ and $ρ_{3}$ (with $ρ_{1} > ρ_{2} > ρ_{3}$ ), having the same value of surface tension $T$ , rise to the same height in three identical capillaries. The angles of contact $θ_{1}, θ_{2}$ and $θ_{3}$ obey [2016]

Q 10 :
Water rises to a height $h$ in capillary tube. If the length of capillary tube above the surface of water is made less than $h$ , then [2015]

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Topic Question Set

Q 2 : A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is 0.07Nm-1, then the excess force required to take it away from the surface is [2024]

Q 3 : Which of the following statement is not true? [2023]

Q 4 : The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = 0.03Nm-1) [2023]

Q 5 : If a soap bubble expands, the pressure inside the bubble [2022]

Q 6 : A capillary tube of radius r is immersed in water and water rises in it to a height h. The mass of the water in the capillary is 5 g. Another capillary tube of radius 2r is immersed in water. The mass of water that will rise in this tube is [2020]

Q 7 : A soap bubble, having radius of 1 mm, is blown from a detergent solution having a surface tension of 2.5×10-2N/m. The pressure inside the bubble equals that at a point Z0 below the free surface of water in a container. Taking g=10m/s2, density of water =103kg/m3, the value of Z0 is [2019]

Q 8 : A rectangular film of liquid is extended from (4cm×2cm) to (5cm×4cm). If the work done is 3×10-4J, the value of the surface tension of the liquid is [2016]

Q 9 : Three liquids of densities ρ1,ρ2 and ρ3 (with ρ1>ρ2>ρ3), having the same value of surface tension T, rise to the same height in three identical capillaries. The angles of contact θ1,θ2 and θ3 obey [2016]

Q 10 : Water rises to a height h in capillary tube. If the length of capillary tube above the surface of water is made less than h, then [2015]

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Q 2 :
A thin flat circular disc of radius 4.5 cm is placed gently over the surface of water. If surface tension of water is $0.07$ ${Nm}^{- 1}$ , then the excess force required to take it away from the surface is [2024]

Q 3 :
Which of the following statement is not true? [2023]

Q 4 :
The amount of energy required to form a soap bubble of radius 2 cm from a soap solution is nearly (surface tension of soap solution = $0.03 N$ $m^{- 1}$ ) [2023]

Q 5 :
If a soap bubble expands, the pressure inside the bubble [2022]

Q 6 :
A capillary tube of radius $r$ is immersed in water and water rises in it to a height $h$ . The mass of the water in the capillary is 5 g. Another capillary tube of radius $2 r$ is immersed in water. The mass of water that will rise in this tube is [2020]

Q 8 :
A rectangular film of liquid is extended from $(4 cm \times 2 cm)$ to $(5 cm \times 4 cm)$ . If the work done is $3 \times 10^{- 4}$ $J$ , the value of the surface tension of the liquid is [2016]

Q 9 :
Three liquids of densities $ρ_{1}, ρ_{2}$ and $ρ_{3}$ (with $ρ_{1} > ρ_{2} > ρ_{3}$ ), having the same value of surface tension $T$ , rise to the same height in three identical capillaries. The angles of contact $θ_{1}, θ_{2}$ and $θ_{3}$ obey [2016]

Q 10 :
Water rises to a height $h$ in capillary tube. If the length of capillary tube above the surface of water is made less than $h$ , then [2015]