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.

HARD

Earn 100

Explain stress versus strain graph with the help of a neat labelled diagram.

Important Questions on Elasticity

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

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>Mechanics>Elasticity>Stress-Strain Curve

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.

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

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

HARD

Physics>Mechanics>Elasticity>Stress-Strain Curve

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:

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

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:

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

The Young's modulus of steel is twice that of brass. Two wires of same length and of same area of cross-section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

Which one of the following is most elastic in nature?

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

HARD

Physics>Mechanics>Elasticity>Stress-Strain Curve

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,

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

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>Mechanics>Elasticity>Stress-Strain Curve

A metal rod of length

L

and cross-sectional area

A

is heated through

T ° C

. What is the force required to prevent the expansion of the rod lengthwise?

[Y

= Young's modulus of the material of rod,

α =

coefficient of linear expansion

]

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

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>Mechanics>Elasticity>Stress-Strain Curve

A rubber cord of density

d,

Young's modulus

Y

and length

L

is suspended vertically. If the cord extends by a length

0.5 L

under its own weight, then

L

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

A load of mass

M kg

is suspended from a steel wire of length

2 m

and radius

1.0 mm

in Searle's apparatus experiment. The increase in length produced in the wire is

4.0 mm .

Now the load is fully immersed in a liquid of relative density

2 .

The relative density of the material of load is

8 .

The new value of increase in length of the steel wire is:

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

A steel rail of length

5 m

and area of cross section

40 {cm}^{2}

is prevented from expanding along its length while the temperature rises by

10 ° C

. If coefficient of linear expansion and Young's modulus of steel are

1.2 \times 10^{- 5} K^{- 1}

and

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

respectively, the force developed in the rail is approximately:

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

In materials like aluminium and copper, the correct order of magnitude of various elastic modulii is :

MEDIUM

Physics>Mechanics>Elasticity>Stress-Strain Curve

One end of a slack wire (Young's modulus,

Y

, length,

L

and cross-sectional area,

A

) is clamped to a rigid wall and the other end to a block (mass

m

) which rests on a smooth horizontal plane. The block is set in motion with a speed,

v

. What is the maximum distance the block will travel after the wire becomes taut?

HARD

Physics>Mechanics>Elasticity>Stress-Strain Curve

Define Bulk modulus.

EASY

Physics>Mechanics>Elasticity>Stress-Strain Curve

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

HARD

Physics>Mechanics>Elasticity>Stress-Strain Curve

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

Explain stress versus strain graph with the help of a neat labelled diagram.

Important Questions on Elasticity

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