It is given by the ratio of pressure applied to the corresponding relative decrease in the volume of the material. Mathematically, it is represented as follows: B = Δ P / ( Δ V / V ) Where: B : Bulk modulus Δ P : change of the pressure or force applied per unit area on the material Δ V : change of the volume of the material due to the compression V : Initial volume of the material.

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The elastic behaviour of a body can be turned into plastic behaviour under the larger deforming force.

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Important Questions on Mechanical Properties of Solids

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Which one of the following is most elastic in nature?

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Calculate the strain energy per unit volume in a brass wire of length $3 m$ and area of cross-section $0.6 m m^{2}$ when it is stretched by $3 m m$ and a force of $6 k g w t$ is applied to its free end.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

The wrong statement in the following is

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Breaking stress of a steel wire is

p

and the density of steel is

ρ

. The greatest length of steel wire that can hang vertically without breaking is

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Young’s moduli of the material of wires A and B are in the ratio of

1 : 4

, while its area of cross sections are in the ratio of

1 : 3

. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires A and B will be in the ratio of [Assume length of wires A and B are same]

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Define Bulk modulus.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A constant force is applied to a metal wire of length

L

. Volume of the wire is constant. The extension produced is proportional to

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A wire of diameter

1 mm

breaks under a tension of

1000 N

. Another wire of the same material as that of the first one, but of diameter

2 mm

breaks under a tension of:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A steel wire is suspended vertically from a rigid support. When the wire is loaded with a weight in air, it is extended by

x_{a}

. When the weight is completely inside the water, the extension becomes

x_{w}

. The relative density of the material of the weight is,

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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:

HARD

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

In plotting stress versus strain curves for two materials

P

and

Q

, a student by mistake puts strain on the

y

-axis and stress on the

x

- axis as shown in the figure. Then the correct statement(s) is(are)

Question Image

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A steel wire of cross-sectional area

4 {cm}^{2}

has elastic limit of

2.2 \times 10^{8} N m^{- 2}

. The maximum upward acceleration that can be given to a

1000 kg

elevator supported by this steel wire if the stress is to exceed one-fourth of the elastic limit is [Take,

g = 10 m s^{- 2}

]

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Two wires of the same material and length but cross sectional area in the ratio

1 : 2

are used to suspend the same loads. The extension in them will be in the ratio

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

With rise in temperature, young's modulus of elasticity _________.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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:

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

Two separate wires

A

and

B

are stretched by

2 mm

and

4 mm

respectively, when they are subjected to a force of

2 N .

Assume that both the wires are made up of same material and the radius of wire

B

4

times that of the radius of wire

A .

The length of the wires

A

and

B

are in the ratio of

a : b .

Then

\frac{a}{b}

can be expressed as

\frac{1}{x}

, where

x

is _____.

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Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

A fixed volume of iron is drawn into a wire of length

‘ L ’

. The extension

‘ x ’

produced in the wire by a constant force

‘ F ’

is proportional to _____.

MEDIUM

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

The elastic limit of brass is

379 M P a

. The minimum diameter of a brass rod if it is to support a

400 N

load without exceeding its elastic limit will be

EASY

Physics>Mechanical Properties of Matter>Mechanical Properties of Solids>Elastic Behaviour of Solids

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

The elastic behaviour of a body can be turned into plastic behaviour under the larger deforming force.

Important Questions on Mechanical Properties of Solids

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