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The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of

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Important Questions on Elasticity

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Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A cube of metal is subjected to a hydrostatic pressure

4 GPa

. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal,

B = 8 \times 10^{10} Pa

)

HARD

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A lift is tied with thick iron ropes having mass

M

. The maximum acceleration of the lift is ‘

a m s^{- 2}

and maximum safe stress is

S N m^{- 2}

. The minimum diameter of the rope is

MEDIUM

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

The length of a metal wire is

l_{1}

when the tension in it is

T_{1}

and is

l_{2}

when the tension is

T_{2}

. The natural length of the wire is,

EASY

Physics>Mechanics>Elasticity>Deformation and 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}

]

EASY

Physics>Mechanics>Elasticity>Deformation and 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

HARD

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A mild steel wire of length $2 L$ and cross-sectional area $A$ is stretched, well with in the elastic limit, horizontally between two pillars as shown in figure. A mass $m$ is suspended from the mid-point of the wire. Strain in the wire is

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Physics>Mechanics>Elasticity>Deformation and 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>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A string of a material of length

1 m,

cross-sectional area

0.2 {cm}^{2}

requires

2000 N

to extend it by

1 mm

. The same material is used to manufacture the legs of a robot of

50 cm

length and of cross-sectional area

0.5 {cm}^{2}

each. The mass of the robot is

50 kg

. When it jumps from a building of height

h

, it experiences a strain

0.05 .

The maximum height through which the robot can jump without breaking its legs is

(g = 10 m s^{- 2})

EASY

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

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?

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Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A body of mass

m = 10 k g

is attached to one end of a wire of length

0.3 m

. What is the maximum angular speed (in

r a d s^{- 1}

) with which it can be rotated about its other end in a space station without breaking the wire?
[Breaking stress of wire

(σ)

= 4.8 \times 10^{7} N m^{- 2}

and area of cross-section of the wire

= 10^{- 2} c m^{2}

]

MEDIUM

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A wire of length

1 m

and radius

2 mm

is vertically clamped. The lower end is twisted through an angle of

45 °

. The angle of shear is _____

EASY

Physics>Mechanics>Elasticity>Deformation and 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:

EASY

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

The speed of the water in a river is

V

near the surface. If the coefficient of viscosity of water is

η

and the depth of the river is

H

, then the shearing stress between the horizontal layers of water is

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Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

A

and

B

are two wires. The radius of

A

is twice that of

B

. They are stretched by the same load. Then the stress on

B

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Physics>Mechanics>Elasticity>Deformation and 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

EASY

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

If a tensile force is suddenly removed from a wire then its temperature will

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Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

Two wires

A

and

B

are stretched by the same load. If the area of cross-section of wire '

A

' is double that of

^{'} B^{'}

, then the stress on '

B

' is

MEDIUM

Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

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}

]

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Physics>Mechanics>Elasticity>Deformation and Elastic Behaviour of Solids

An elevator of mass

m

is connected to a rope which pulls the elevator up with a maximum acceleration equal to

a

. If the maximum bearable tension in the rope is

T

, then for a safe journey the minimum diameter of the rope is [

g

= acceleration due to gravity]

MEDIUM

Physics>Mechanics>Elasticity>Deformation and 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

The longitudinal extension of any elastic material is very small. In order to have an appreciable change, the material must be in the form of

Important Questions on Elasticity

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