EASY

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Write two applications of elastic behaviour of the material.

Important Questions on Properties of Solid and Liquid

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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 $5 \times 10^{- 4}$ .

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EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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:

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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}

)

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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}

]

HARD

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

]

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

An aluminium rod with Young’s modulus

Y = 7.0 \times 10^{10} N m^{- 2}

undergoes elastic strain of

0.04 %

. The energy per unit volume stored in the rod in

SI

unit

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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:

MEDIUM

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area

a

floats on the surface of the liquid, covering entire cross-section of cylindrical container. When a mass m is placed on the surface of the piston to compress the liquid, the fractional decrement in the radius of the sphere

(\frac{d r}{r})

, is:

EASY

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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

HARD

Physics>Mechanics>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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>Properties of Solid and Liquid>Young’s Modulus

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?

Write two applications of elastic behaviour of the material.

Important Questions on Properties of Solid and Liquid

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