${X}$ and ${Y}$ are two capillary tubes with lengths ${l}_{{X}}$ and $l_Y$ and with radii $r_X$ and $r_Y$ respectively. When a pressure difference $P$ is maintained between the ends of $X$, the rate of flow of water through $X$ is $10\, \mathrm{cc} / \mathrm{sec}$. ${X}$ and ${Y}$ are now connected in series and the same pressure difference $P$ is maintained across the combination. If $l_{\mathrm{X}}=2 l_{\mathrm{Y}}$ and ${r}_{{X}}={r}_{{Y}}$, rate of flow of water through the combination will be:

$\frac{52}{7}\, \mathrm{cc} / \mathrm{sec}$

$\frac{9}{4}\, \mathrm{cc} / \mathrm{sec}$

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NEET • PHYSICS • MECHANICAL PROPERTIES OF FLUIDS

Mechanical properties of fluids practice · Hard

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1 Hard

1 of 22

Application +4 | -1

At a depth of

3 {~km}

in an ocean, what is the force acting on a window of area

30 {~cm} \times 25 {~cm}

of a submarine, the interior of submarine is maintained at sea level atmospheric pressure? (The density of sea water is

1030 {~kg} {~m}^{-3}, g=10 {~m} / {s}^2

)

View answer and explanation

Correct option: C

2.32 \times 10^6 {~N}

Option C (

2.32 \times 10^6 {~N}

) is correct because it is the force calculated from the pressure difference at the given depth and the area of the window.

2 Hard

2 of 22

Application +4 | -1

If velocity of a liquid in streamline flow is

2 {~m} / {s}

, then velocity head is

View answer and explanation

Correct option: C

0.2 {~m}

Option C (

0.2 {~m}

) is correct because the velocity head is calculated using the formula

v^2 / (2g)

, where v is the velocity and g is the acceleration due to gravity.

3 Hard

3 of 22

Application +4 | -1

What is depth of lake at which density of water is 2% greater than that at surface. Compressibility of water is

25\mathrm{ } \times \mathrm{ }{10^{ - 6}}/atm

View answer and explanation

Correct option: D

8 km

Option D (8 km) is correct because the depth is calculated using the compressibility of water and the change in density due to pressure.

4 Hard

4 of 22

Application +4 | -1

A tank having cross sectional area

64 {A}

is filled with water to a height

4 {h}

. If a small hole of cross sectional area

{A}

is made at the bottom of the tank, then the time taken by the water level to decrease from

16 {h}

4{h}

View answer and explanation

Correct option: D

128 \sqrt{\frac{2h}{g}}

Option D (

128 \sqrt{\frac{2h}{g}}

) is correct because it is derived from Torricelli's law and integrating the flow rate over the changing height.

5 Hard

5 of 22

Understanding +4 | -1

Given below are two statements: One is labelled as
Assertion (A) and the other· is labelled as Reason
(R).
Assertion (A) : Clothes containing oil or grease
stains cannot be cleaned by water wash.
Reason (R) : Because the angle of contact
between the oil/ grease and water is obtuse.
In the light of the above statements, choose the
correct answer from the option given below.

View answer and explanation

Correct option: A

Both (A) and (R) are true and (R) is the correct
explanation of (A)

Option A (Both (A) and (R) are true and (R) is the correct explanation of (A)) is correct because oil and grease are non-polar substances, and water is a polar substance. The obtuse angle of contact indicates poor wetting, preventing water from effectively cleaning the stains.

6 Hard

6 of 22

Remembering +4 | -1

The onset of turbulence in a liquid is determined by

View answer and explanation

Correct option: C

Reynold’s number

Option C (Reynold’s number) is correct because the transition from laminar to turbulent flow is determined by the Reynolds number.

7 Hard

7 of 22

Application +4 | -1

A spherical ball of radius

1 \times 10^{-4} \mathrm{~m}

and density

10^5

\mathrm{kg} / \mathrm{m}^3

falls freely under gravity through a distance

h

before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of

h

is approximately :

(The coefficient of viscosity of water is

9.8 \times 10^{-6}

\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)

View answer and explanation

Correct option: C

2518 \mathrm{~m}

Option C (

2518 \mathrm{~m}

) is correct because it is calculated by equating the weight of the ball to the viscous force when terminal velocity is reached, and then using kinematics to find the height.

8 Hard

8 of 22

Application +4 | -1

The absolute pressure acting on a horizontal submarine is

4 \times 10^5 \mathrm{~Pa}

at a certain depth of ocean. If the depth of submarine is doubled, the percentage increase in the absolute pressure acting on the submarine would be:

(1 atm

=10^5

Pascal,

g=10 \mathrm{~m} / \mathrm{s}^2,

\rho_w=10^3 \mathrm{~kg} / \mathrm{m}^3)

View answer and explanation

Correct option: B

0.75

Option B (0.75) is correct because doubling the depth increases the pressure due to water, and the percentage increase is calculated relative to the initial absolute pressure.

9 Hard

9 of 22

Application +4 | -1

Capillaries of length

\ell

and

2 \ell

are connected in series. Their radii are

r

and

2 r

respectively. If stream line but viscous flow is maintained and pressure difference across first and second capillaries are

{P}_1

and

{P}_2

respectively. Then the ratio

\frac{P_1}{P_2}

will be

View answer and explanation

Correct option: A

Option A (8) is correct because the pressure difference is proportional to the length and inversely proportional to the fourth power of the radius. By calculating the flow rate and pressure drop across each capillary, the ratio can be determined.

10 Hard

10 of 22

Application +4 | -1

A raft of wood of density

600 \mathrm{~kgm}^{-3}

and mass

120 \mathrm{~kg}

floats in water. How much weight (in

\mathrm{kg}

) can be put on the raft to make it just sink?

View answer and explanation

Correct option: A

Option A (80) is correct because it calculates the additional weight needed to fully submerge the raft, based on buoyancy principles.

11 Hard

11 of 22

Application +4 | -1

A small block of wood of specific gravity 0.5 is submerged at a depth of

1.2 \mathrm{~m}

in a vessel filled with water. The vessel is accelerated upwards with an acceleration

a_0=\frac{g}{2}

. Time taken by the block to reach the surface, if it is released with zero initial velocity is

\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)

View answer and explanation

Correct option: B

0.4 \mathrm{~s}

Option A (

0.6 \mathrm{~s}

) is correct because it is the calculated time taken by the block to reach the surface, considering the upward acceleration of the vessel.

12 Hard

12 of 22

Application +4 | -1

An iceberg is floating in water. The density of ice in the iceberg is

917\mathrm{kg}{\mathrm{m}^{ - 3}}

and the density of water is

1024\mathrm{kg}{\mathrm{m}^{ - 3}}

View answer and explanation

Correct option: B

0.1

Option B (0.1) is correct because it represents the fraction of the iceberg that is above the water, calculated using the densities of ice and water.

13 Hard

13 of 22

Application +4 | -1

A cylindrical vessel filled with water upto a height

h

weighs

w

and is resting on a horizontal plane. The side of wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of the vessel and the plane is

\mu

. The minimum diameter of the hole so that the vessel just begins to move on the floor after the removal of the plug is:

View answer and explanation

Correct option: D

\sqrt{\frac{2 \mu w}{\pi \rho h g}}

Option D (

\sqrt{\frac{2 \mu w}{\pi \rho h g}}

) is correct because it equates the frictional force with the thrust force due to the water exiting the hole, considering the weight of the water and the height.

14 Hard

14 of 22

Application +4 | -1

A stone of mass

10 \mathrm{~kg}

is lying at the bed of a large lake

10 \mathrm{~m}

deep. If the relative density of the stone is 2, the amount of work done by external force to bring slowly it at the surface of the lake will be (neglect all resistive forces)

View answer and explanation

Correct option: A

490 \mathrm{~J}

Option A (

490 \mathrm{~J}

) is correct because the work done is equal to the change in potential energy, which is the difference between the weight of the stone and the buoyant force, multiplied by the depth.

15 Hard

15 of 22

Analyzing +4 | -1

An iron block is on a boat which floats in a pond. The block is thrown into the water. The level of water in the pond will be

View answer and explanation

Correct option: B

less than the earlier level

Option B (less than the earlier level) is correct because the iron block displaces less water when submerged than when it was in the boat.

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16 Hard

16 of 22

Application +4 | -1

Rain drops of radius '

r

' having a mass '

{m}

' is falling with terminal velocity. The rate of energy dissipation due to viscous force is proportional

View answer and explanation

Correct option: C

{m}^{5 / 3}

Option C is correct because the rate of energy dissipation is proportional to the terminal velocity squared and mass to the power of 5/3.

17 Hard

17 of 22

Application +4 | -1

A sphere of relative density

\sigma

and diameter

D

has concentric cavity of diameter

{d}

. The ratio of

\frac{{D}}{{d}}

, if it just floats on water in a tank is:

View answer and explanation

Correct option: A

\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}

Option A (

\left(\frac{\sigma}{\sigma-1}\right)^{\frac{1}{3}}

) is correct because it represents the ratio of diameters when the buoyant force equals the weight of the sphere.

18 Hard

18 of 22

Understanding +4 | -1

When two capillary tubes of different diameters are dipped vertically, the rise of the liquid is

View answer and explanation

Correct option: D

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