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A bucket contains water filled upto a height= 15 cm. The bucket is tied to a rope which is passed over a frictionless light pulley and the other end of the rope is tied to a weight of mass which is half of that of the (bucket+water). The water pressure above the atmospheric pressure at the bottom is

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Important Questions on Fluid Mechanics

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Physics>Mechanics>Fluid Mechanics>Pascal’s Law

The approximate depth of an ocean is

2700 m

. The compressibility of water is

45.4 \times 10^{- 11} P a^{- 1}

and density of water is

10^{3}

{kg/m}^{3}

. What fractional compression of water will be obtained at the bottom of the ocean ?

MEDIUM

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A uniform cylinder of length

L

and mass

M

having cross-sectional area

A

is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density

σ

at equilibrium position. The extension

x_{0}

of the spring when it is in equilibrium is :

MEDIUM

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A body of density

ρ

and volume

V

is lifted through height

h

in a liquid of density

σ (< ρ) .

The increase in potential energy of the body is

MEDIUM

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A submarine experiences a pressure of

5.05 \times 10^{6} P a

at a depth of

d_{1}

in a sea. When it goes further to a depth of

d_{2}

, it experiences a pressure of

8.08 \times 10^{6} P a

. Then

d_{2} - d_{1}

is approximately (density of water

= 10^{3} k g / m^{3}

and acceleration due to gravity

= 10 m s^{- 2}

EASY

Physics>Mechanics>Fluid Mechanics>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

MEDIUM

Physics>Mechanics>Fluid Mechanics>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:

HARD

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A cylindrical block of wood (density = $650 kg m^{- 3}$ ), of base area $30 {cm}^{2}$ and height $54 cm$ , floats in a liquid of density $900 kg m^{- 3}$ . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :

EASY

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

An aluminium sphere is dipped into water. Which of the following is true?

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Physics>Mechanics>Fluid Mechanics>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>Fluid Mechanics>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}]

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Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A cubical block of side

0.5 m

floats on water with

30 %

of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water

= 10^{3} k g / m^{3}

]

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Physics>Mechanics>Fluid Mechanics>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):

HARD

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

A wooden block floating in a bucket of water has

\frac{4}{5}

of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is:

MEDIUM

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

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>Mechanics>Fluid Mechanics>Pascal’s Law

Consider a solid sphere of radius

R

and mass density

ρ (r) = ρ_{0} (1 - \frac{r^{2}}{R^{2}}), 0 < r \leq R .

The minimum density of a liquid in which it will float is:

HARD

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

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

EASY

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

The density of kerosene is

800 kg m^{- 3}

. Its relative density is

EASY

Physics>Mechanics>Fluid Mechanics>Pascal’s Law

Two non-mixing liquids of densities

ρ

and

n ρ (n > 1)

are put in a container. The height of each liquid is

h.

A solid cylinder of length

L

and density

d

is put in this container. The cylinder floats with its axis vertical and length

p L (p < 1)

in the denser liquid. The density

d

is equal to:

HARD

Physics>Mechanics>Fluid Mechanics>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 :

Question Image

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Physics>Mechanics>Fluid Mechanics>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:

Important Questions on Fluid Mechanics

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