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Pressure exerted by a liquid depends upon :

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Important Questions on Force and Pressure

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

A machine is blowing spherical soap bubbles of different radii filled with helium gas. It is found that if the bubbles have a radius smaller than

1 cm

, then they sink to the floor in still air. Larger bubbles float in the air. Assume that the thickness of the soap film in all bubbles is uniform and equal. Assume that the density of soap solution is the same as that of water

(1000 kg m^{- 3}) .

The density of helium inside the bubbles and air are

0.18 kg m^{- 3} & 1.23 kg m^{- 3}

, respectively. Then the thickness of the soap film of the bubbles is

(1 μm = 10^{- 6} m)

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

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}

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

A box, when hung from a spring balance shows a reading of

50 kg

. If the same box is hung from the same spring balance inside an evacuated chamber, the reading on the scale will be

HARD

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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) :

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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}

]

EASY

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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

Science>Physics>Force and Pressure>Pressure of Liquid

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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

Science>Physics>Force and Pressure>Pressure of Liquid

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

EASY

Science>Physics>Force and Pressure>Pressure of Liquid

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

HARD

Science>Physics>Force and Pressure>Pressure of Liquid

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

190 mm

Hg

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

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:

MEDIUM

Science>Physics>Force and Pressure>Pressure of Liquid

A block of mass

3 kg

and density

ρ

, suspended from a spring balance is immersed in a liquid of density

\frac{ρ}{3}

. Then the balance would read weight as:

Pressure exerted by a liquid depends upon :

Important Questions on Force and Pressure

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