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A uniform metallic bar of mass $m,$ length $L$ and cross-sectional area $A$ is acted upon by force $2 F, F$ as shown in the figure acting along its length. There is no friction between the bar and the ground. Young's modulus of elasticity of the material of the bar is $Y$ .

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Important Questions on Elasticity

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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

Question Image

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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?

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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

EASY

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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}

]

MEDIUM

Physics>Mechanics>Elasticity>Hooke's Law and Modulus of Elasticity

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>Hooke's Law and Modulus of Elasticity

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

A uniform metallic bar of mass m, length L and cross-sectional area A is acted upon by force 2F, F as shown in the figure acting along its length. There is no friction between the bar and the ground. Young's modulus of elasticity of the material of the bar is Y.

Important Questions on Elasticity

Learn and Prepare for any exam you want !

A uniform metallic bar of mass $m,$ length $L$ and cross-sectional area $A$ is acted upon by force $2 F, F$ as shown in the figure acting along its length. There is no friction between the bar and the ground. Young's modulus of elasticity of the material of the bar is $Y$ .