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The value of isothermal bulk modulus of a gas is equal to

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Important Questions on Elasticity

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The bulk modulus of a liquid is

3 \times 10^{9} N m^{- 2}

The pressure required to reduce the given volume of this liquid by

1 %

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The normal density of a material is

ρ

and its bulk modulus of elasticity is

K

. The magnitude of increase in density of material, when a pressure

P

is applied uniformly on all sides, will be :

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

When a rubber ball is taken to a depth of _______

m

in deep sea, its volume decreases by

0.5 %

(The bulk modulus of rubber

= 9.8 \times 10^{8} N m^{- 2}

Density of sea water

= 10^{3} kg m^{- 3}

g = 9.8 m s^{- 2}

)

HARD

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The compressibility of a substance is the reciprocal of ____.

HARD

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A bottle has an opening of radius

a

and length

b

. A cork of length

b

and radius

(a + ∆ a)

where

(∆ a ≪ a)

, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is

B

and the coefficient of friction between the bottle and cork is

μ

, then the force needed to push the cork into the bottle is

Question Image

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The radius of a sphere is found to have reduced by

0.01 %

, when measured at a depth

' H'

of the sea. If the bulk modulus of elasticity of the material of sphere is

4 \times 10^{10} N m^{- 2}

and density of water is

1000 kg m^{- 3}

, find the value of

H

' (use

g = 10 m s^{- 2})

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

An object is located at $2 km$ beneath the surface of the water. If the fractional compression $\frac{Δ V}{V}$ is $1.36 %$ , the ratio of hydraulic stress to the corresponding hydraulic strain will be ______[Given: density of water is $1000 kg m^{- 3}$ and $g = 9.8 {m s}^{- 2} .$

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A certain pressure '

P

' is applied to

1

litre of water and

2

litre of a liquid separately. Water gets compressed to

0.01 %

whereas the liquid gets compressed to

0.03 %

. The ratio of Bulk modulus of water to that of the liquid is

\frac{3}{x}

. The value of

x

is ______.

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A cubical solid aluminum

(bulk modulus = - V \frac{d P}{d V} = 70 GPa)

block has an edge length of

1 m

on the surface of the earth. It is kept on the floor of a

5 km

deep ocean. Taking the average density of water and the acceleration due to gravity to be

10^{3} kg m^{- 3}

and

10 m s^{- 2}

, respectively, the change in the edge length of the block in

mm

is ________.

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

What is the pressure required to reduce the given volume of water by

1 %

? (Bulk modulus

(K) = 2 \times 10^{8} N m^{- 2}

)

HARD

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

Define Young’s modulus.

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The bulk modulus of a liquid is

3 \times 10^{10} {Nm}^{- 2}

. The pressure required to reduce the volume of liquid by

2 %

is :

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A body is subjected to stress resulting in the change in volume of the body. The stress must be

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A swimming pool has a depth of

22 m

and area

700 m^{2}

. Calculate fractional change

\frac{Δ v}{v}

of water at the bottom of the swimming pool. Given that the bulk modulus of water is

2.2 \times 10^{9} {Nm}^{- 2}, g = 10 m s^{- 2}

, and density of water

1000 kg m^{- 3}

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

Pressure for polytropic process $P$ varies with volume $V$ as $P = a V^{- 3}$ , Find out the bulk modulus.

EASY

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

The wrong statement in the following is

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area

a

floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere

(\frac{d r}{r})

, is:

HARD

Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

An external pressure

P

is applied on a cube at

0 ° C

so that it is equally compressed from all sides.

K

is the bulk modulus of the material of the cube and

α

is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

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Physics>Mechanical Properties of Matter>Elasticity>Elasticity of Gases

A gas undergoes a process in which the pressure and volume are related by

{V P}^{n} = c o n s t a n t

. The bulk modulus of the gas is -

The value of isothermal bulk modulus of a gas is equal to

Important Questions on Elasticity

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