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Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force will be in the ratio.

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Important Questions on Elasticity

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

If $S$ is stress and

Y

is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

HARD

Physics>Mechanics>Elasticity>Elastic Potential Energy

A stone of mass

20 g

is projected from a rubber catapult of length

0.1 m

and area of cross section

10^{- 6} m^{2}

stretched by an amount

0.04 m .

The velocity of the projected stone is

m s^{- 1} .

(Young's modulus of rubber

= 0.5 \times 10^{9} N m^{- 2}

)

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

What is the elastic potential energy stored in a stretched steel wire of length

4 m .

The wire is stretched through

4 mm

and consists of cross-sectional area of

8 {mm}^{2} .

(Young's modulus of steel

= 2.0 \times 10^{11} N m^{- 2}

)

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

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:

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

A wire of length

L

and area of cross section

A

is made of material of Young’s modulus

Y

. It is stretched by an amount

x

. The work done in stretching the wire is

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

The area of cross section of the rope used to lift a load by a crane is

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

. The maximum lifting capacity of the crane is

10

metric tons. To increase the lifting capacity of the crane to 25 metric tons, the required area of cross section of the rope should be
(take

g = 10 {ms}^{- 2}

)

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

A wire of Young's modulus

Y

is subjected to a stress

S

. The elastic potential energy per unit volume of the wire is given by

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

For a perfectly rigid body,

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is

1 : 4,

the ratio of their diameters is:

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

Consider a metallic wire of length

10 m

. An external force applied results in an elongation of

5 mm

. What is the potential energy stored per unit volume
[Young's modulus of wire

Y = 16 \times 10^{10} N m^{- 2}

]

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

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

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

When a block of mass

M

is suspended by a long wire of length

L

, the length of the wire becomes

(L + l) .

The elastic potential energy stored in the extended wire is

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

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>Elastic Potential Energy

The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5 \times 10^{- 4}$ is _____ $kJ m^{- 3}$ . Assume that material is elastic upto the linear strain of $5 \times 10^{- 4}$ .

Question Image

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

Copper of fixed volume

V

is drawn into wire of length

l

. When this wire is subjected to a constant force

F,

the extension produced in the wire is

∆ l .

Which of the following graph is a straight line?

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

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

)

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

A metallic rod breaks when strain produced is

0.2 %

. Young's modulus of the material of the rod is

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

. What should be its area of cross-section to support a load of

10^{4} N

EASY

Physics>Mechanics>Elasticity>Elastic Potential Energy

S

is the stress and

Y

is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

A boy’s catapult is made of rubber cord which is

42 c m

long, with

6 m m

diameter of cross-section and of negligible mass. The boy keeps a stone weighing

0.02 k g

on it and stretches the cord by

20 c m

by applying a constant force. When released, the stone flies off with a velocity of

20 m s^{- 1}

. Neglect the change in the area of cross-section of the cord while stretched. The Young’s modulus of rubber is closest to:

MEDIUM

Physics>Mechanics>Elasticity>Elastic Potential Energy

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?

Two wires of the same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The elastic potential energy per unit volume for the wires, when stretched by the same force will be in the ratio.

Important Questions on Elasticity

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