EASY

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Two syringes of different cross-section (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1 cm$ and $3 cm$ respectively. If a force of $10 N$ is applied to the smaller piston then the force exerted on the larger piston is

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Important Questions on Mechanical Properties of Fluids

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A healthy adult of height

1.7 m

has an average blood pressure (BP) of

100 mm

Hg

. The heart is typically at a height of

1.3 m

from the foot. Take, the density of blood to be

10^{3} kg / m^{3}

and note that

100 mm

Hg

is equivalent to

13.3 kPa

(kilo pascals). The ratio of BP in the foot region to that in the head region is close to

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is

5 cm

and its rotational speed is

2

rotations per second, then the difference in the heights between the center and the sides, in

cm,

will be:

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

Water stands upto height $' h'$ behind the dam as shown in the figure. The front view of the dam gate is also shown in the adjoining figure. Density of water is $' ρ'$ and acceleration due to gravity is $' g'$ . If atmospheric pressure force is also considered, the point of application of total force acting on the dam due to water above $' o'$ is_____

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MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

Consider two wires of same material having their ratio of radii to be

2 : 1

. If these two wires are stretched by equal force, the ratio of stress produced in them is :

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A hydraulic press can lift

100 kg

when a mass

m

is placed on the smaller piston.How much mass (in

k g

) can it lift when the diameter of the larger piston is increased by

4

times and that of the smaller piston is decreased by

4

times keeping the same mass

m

on the smaller piston.

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A submarine has a window of area

30 \times 30 {cm}^{2}

on its ceiling and is at a depth of

100 m

below sea level in a sea. If the pressure inside the submarine is maintained at the sea-level atmosphere pressure, then the force acting on the window is (consider density of sea water

= 1.03 \times 10^{3} kg m^{- 3}

acceleration due to gravity

= 10 m s^{- 2}

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

There is a circular tube in a vertical plane. Two liquids which do not mix and of densities d₁ and d₂ are filled in the tube. Each liquid subtends 90^o angle at centre. Radius joining their interface makes an angle

α

with vertical. Ratio

\frac{d_{1}}{d_{2}}

is:

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A spherical marble of radius $1 cm$ is stuck in a circular hole of radius slightly smaller than its own radius (for calculation purpose, both can be taken same) at the bottom of a bucket of height $40 cm$ and filled with water up to $10 cm$ . If the mass of the marble is $20 g$ , the net force on the marble due to water is close to

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HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

Two narrow bores of diameter

5.0 mm

and

8.0 mm

are joined together to form a

U -

shaped tube open at both ends. If this

U -

tube contains water, what is the difference in the level of two limbs of the tube.
[Take surface tension of water

T = 7.3 \times 10^{- 2} N m^{- 1}

, angle of contact

= 0, g = 10 {m s}^{- 2}

and density of water

= 1.0 \times 10^{3} kg m^{- 3}]

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A nurse measures the blood pressure of a seated patient to be

190 mm

Hg

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

The pressure acting on a submarine is

3 \times 10^{5} Pa

at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be: (Assume that atmospheric pressure is

1 \times 10^{5} Pa

density of water is

10^{3} kg m^{- 3}, g = 10 {ms}^{- 2}

)

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is $5 cm$ and the angular speed of rotation is $ω rad s^{- 1}$ . The difference in the height, $h (in cm)$ of liquid at the Centre of vessel and at the sides of the vessel will be :

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EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

The liquid shown in the figure in the two arms is mercury (specific gravity $13.6$ ) and water. If the difference of heights of the mercury column is $2 cm$ , the height $h$ of the water column is

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EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

The pressure at the bottom of a liquid tank is not proportional to the

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

U

-shaped tube is partially filled with an incompressible liquid of density

1.2 g {cm}^{- 3} .

Oil which does not mix with the liquid is next poured into the left side of the

U

-tube until the liquid rises by,

15 cm

on the right side of

U

-tube. If the density of the oil is

0.9 g {cm}^{- 3},

the oil level will stand higher than the liquid level of the right side of

U

-tube by

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A long container has a square base of side

L

. The height to which water should be filled so that the force on one of its side surface is the same as that at its bottom is (ignore atmospheric pressure)

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

The pressure at the bottom of a tank of liquid is not proportional to

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

A tall tank filled with water has an irregular shape as shown. The wall,

C D

makes an angle of,

45^{o}

with the horizontal; the wall,

A B

is normal to the base,

B C

. The lengths,

A B

and,

C D

are much smaller than the height,

h

of water (figure not to scale).
Question Image

Let

P_{1}, P_{2}

and

P_{3}

be the pressures exerted by the water on the wall

A B

, base

B C

, and the wall

C D

, respectively. The density of water is,

ρ

and,

g

is the acceleration due to gravity. Then, approximately

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

One ton stone is put on a larger piston of diameter

40 cm

of a hydraulic lift and a pressure

P

has to be applied on the smaller piston of diameter

2 cm

, to lift the stone. The pressure

P

, is approximately

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pascal's Law

Question Image
Two liquids of densities $ρ_{1}$ and $ρ_{2} (ρ_{2} = 2 ρ_{1})$ are filled up behind a square wall of side $10 m$ as shown in figure. Each liquid has a height of $5 m .$ The ratio of the forces due to these liquids exerted on upper part $M N$ to that at the lower part $N O$ is (Assume that the liquids are not mixing):

Important Questions on Mechanical Properties of Fluids

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