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A bottle is kept on the ground as shown in the figure. The bottle can be modelled as having two cylindrical zones. The lower zone of the bottle has a cross-sectional radius of $R \sqrt{2}$ and is filled with honey of density $2 ρ$ . The upper zone of the bottle is filled with the water of density $ρ$ and has a cross- sectional radius $R$ . The height of the lower zone is $H$ while that of the upper zone is $2 H$ . If now the honey and the water parts are mixed together to form a homogeneous solutions: ( Assume that total volume does not change)

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Important Questions on Mechanical Properties of Fluids

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

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} =

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

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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):

HARD

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

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

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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

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

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>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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HARD

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

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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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:

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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})

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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:

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

The dimensions for pressure is

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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HARD

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

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 :

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

A cylindrical tube, with its base as shown in the figure., is filled with water. It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $θ = 45 °$ . $P_{1}$ and $P_{2}$ are pressures at point $1$ and $2$ , respectively, located at the base of the tube. Let $β = \frac{(P_{1} - P_{2})}{(ρ g d)}$ , where $ρ$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is (are) correct?

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HARD

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

Two spheres

P

and

Q

of equal radii have densities

ρ_{1}

and

ρ_{2}

, respectively. The spheres are connected by a massless string and placed in liquids

L_{1}

and

L_{2}

of densities

σ_{1}

and

σ_{2}

and viscosities

η_{1}

and

η_{2}

, respectively. They float in equilibrium with the sphere

P

L_{1}

and sphere

Q

L_{2}

and the string being taut (see figure). If sphere

P

alone in

L_{2}

has terminal velocity

{\vec{V}}_{P}

and

Q

alone in

L_{1}

has terminal velocity

{\vec{V}}_{Q}

, then

MEDIUM

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

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

The density of kerosene is

800 kg m^{- 3}

. Its relative density is

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

10 {c m}^{3}

cube floats in water with a volume of

4 {c m}^{3}

remaining above the surface. The density of the material form which the cube is made is

MEDIUM

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

In making an alloy, a substance of specific gravity

s_{1}

and mass

m_{1}

is mixed with another substance of specific gravity

s_{2}

and mass

m_{2}

; then the specific gravity of the alloy as

Important Questions on Mechanical Properties of Fluids

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