The wall of a dam is straight with height H and length L . It holds a lake of water on one side of height h ( h < H ) and base dimension L × L . Let the density of water be ρ w . Ignore atmospheric pressure. Then due to the water

the force on the wall is ρ w g L h 2 / 2

the torque about the bottom on the wall is ρ w g L h 3 / 3

the force on the wall is ρ w g L h 2

The wall of a dam is straight with height H and length L . It holds a lake of water on one side of height h ( h < H ) and base dimension L × L . Let the density of water be ρ w . Ignore atmospheric pressure. Then due to the water

the force on the wall is ρ w g L h 2 / 2

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The wall of a dam is straight with height $H$ and length $L$ . It holds a lake of water on one side of height $h (h < H)$ and base dimension $L \times L$ . Let the density of water be $ρ_{w}$ . Ignore atmospheric pressure. Then due to the water

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Important Questions on Mechanical Properties of Fluids

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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 :

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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}

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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

190 mm

Hg

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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>Pressure Inside a Fluid

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

HARD

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, Whose densities are

ρ_{1}

and

ρ_{2} (ρ_{1} > ρ_{2}),

fill half the circle. The angle

θ

between the radius vector passing through the common interface and the vertical is:

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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).
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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

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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>Pressure Inside a Fluid

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

Question Image

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

The dimensions for pressure is

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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>Pressure Inside a Fluid

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}

)

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

Given below are two statements:

Statement I: Pressure in a reservoir of water is same at all points at the same level of water.

Statement II: The pressure applied to enclosed water is transmitted in all directions equally.

In the light of the above statements, choose the correct answer from the options given below:

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

U

tube with both ends open to the atmosphere is partially filled with water. Oil, which is immiscible with water, is poured into one side until it stands at a distance of

10 mm

above the water level on the other side. Meanwhile, the water rises by

65 mm

from its original level (see diagram). The density of the oil is ____

(ρ_{w} = 1000 kg m^{- 3})

MEDIUM

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

A cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $ρ_{w}$ ) and its neck is filled with immiscible oil (density $ρ_{0}$ ). Then the pressure at;
Question Image

EASY

Physics>Mechanics>Mechanical Properties of Fluids>Pressure Inside a Fluid

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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