EASY

Earn 100

Two syringes of different cross-section (without needle) filled with water are connected with a tightly fitted rubber tube filled with water. Diameters of the smaller piston and larger piston are $1 cm$ and $3 cm$ respectively. If a force of $10 N$ is applied to the smaller piston then the force exerted on the larger piston is

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Important Questions on Mechanical Properties of Fluids

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

A man grows into a giant such that his linear dimensions increase by a factor of

9 .

Assuming that his density remains same, the stress in the leg will change by a factor of:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

A particle of mass

1 kg

is moving in SHM with a path length of

0.01 m

and frequency of

50 Hz

. The maximum force in newton, acting on the particle is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

The following observations were taken for determining surface tension

T

of water by capillary method:

diameter of capillary,

D = 1.25 \times 10^{- 2} m

rise of water,

h = 1.45 \times 10^{- 2} m

Using

g = 9.80 m s^{- 2}

and the simplified relation

T = \frac{r h g}{2} \times 10^{3} N m^{- 1}

the possible error in surface tension is closest to:

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see figure). Through a hole of radius r

(r < < R)

at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

One end of a horizontal thick copper wire of length

2 L

and radius

2 R

is welded to an end of another horizontal thin copper wire of length

L

and radius

R

. When the arrangement stretched by applying forces at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

A rectangular film of liquid is extended from

(4 cm \times 2 cm)

(5 cm \times 4 cm)

. If the work done is

3 \times 10^{- 4} J

, the value of the surface tension of the liquid is

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

In an experiment, brass and steel wires of length

1 m

each with areas of cross section

1 m m^{2}

are used. The wires are connected in series and one end of the combined wire is connected to a rigid support and other end is subjected to elongation. The stress required to produce a net elongation of

0.2 m m

is,
[Given, the Young's Modulus for steel and brass are, respectively,

120 \times 10^{9} N / m^{2}

and

60 \times 10^{9} N / m^{2}

]

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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>Mechanical Properties of Matter>Mechanical Properties of Fluids>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}]

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

0.27 g

of a long chain fatty acid was dissolved in

100 {c m}^{3}

of hexane.

10 m L

of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed. The distance from edge to centre of the watch glass is

10 c m

. What is the height of the monolayer?
[Density of fatty acid

= 0.9 g c m^{- 3}; π = 3]

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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):

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

A steel wire having a radius of

2.0 m m

, carrying a load of

4 k g,

is hanging from a ceiling. Given that

g = 3.1 π m s^{- 2},

what will be the tensile stress that would be developed in the wire?

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

When one end of the capillary is dipped in water, the height of the water column is

h

. The upward force of

105 dyne

due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary is
(Surface tension of water

= 7 \times 10^{- 2} N m^{- 1})

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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}

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

Speed of a transverse wave on a straight wire (mass

6.0 g,

length

60 c m

and area of cross-section

1.0 m m^{2}

90 {m s}^{- 1}

. If the Young's modulus of wire is

16 \times 10^{11} N m^{- 2}

, the extension of wire over its natural length is:

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

Which one of the following statement is correct?

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>Pascal's Law

Assume that a drop of a liquid evaporates by a decrease in its surface energy so that its temperature remains unchanged. The minimum radius of the drop for this to be possible is. (The surface tension is

T

, the density of the liquid is

ρ

and

L

is its latent heat of vaporisation.)

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Fluids>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 Mechanical Properties of Fluids

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