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A mercury barometer has a cylindrical capillary tube of radius $r = \sqrt{2} mm$ inverted vertically on the mercury in the trough. Atmospheric pressure is $76 cm$ of mercury but the level of mercury in the capillary is $75 cm$ . The portion of the tube without mercury is $10 cm$ in length. Considering that this region is occupied by ideal gasses, the number of moles of the ideal gas will be : (Given: Temperature $= 37 ° C$ )

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Important Questions on Mechanical Properties of Fluids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

Consider a vessel filled with a liquid upto height

H .

The bottom of the vessel lies in the

X - Y

plane passing through the origin. The density of the liquid varies with

Z

-axis as

ρ (z) = ρ_{0} [2 - {(\frac{z}{H})}^{2}]

. If

P_{1}

and

P_{2}

are the pressures at the bottom surface and top surface of the liquid, the magnitude of

(P_{1} - P_{2})

is :

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

Two thin circular discs

A

and

B

of radii

2 cm

and

4 cm

are in a liquid at the same depth.

T_{A}

is the thrust on

A

and

T_{B}

thrust on

B

. Then

T_{A} : T_{B} =

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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})

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

A barometer is constructed using a liquid (density $= 760 kg m^{- 3}$ ). What would be the height of the liquid column, when a mercury barometer reads $76 cm ?$

(density of mercury $= 13600 kg m^{- 3}$ )

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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

Question Image

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

The density of kerosene is

800 kg m^{- 3}

. Its relative density is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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}

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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_____

Question Image

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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}

)

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

A glass flask weighing

390 g

, having internal volume

500 cc

just floats when half of it is filled with water. Specific gravity of the glass is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

The dimensions for pressure is

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

An open-ended U-tube of uniform cross-sectional area contains water (density $10^{3} kg m^{- 3}$ ). Initially the water level stands at $0.29 m$ from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800 kg m^{- 3}$ is added to the left arm until its length is $0.1 m$ , as shown in the schematic figure below. The ratio $(\frac{h_{1}}{h_{2}})$ of the heights of the liquid in the two arms is

Question Image

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Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Atmospheric Pressure and Gauge Pressure

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

190 mm

Hg

Important Questions on Mechanical Properties of Fluids

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