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If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient $η,$ the Poisson's ratio $σ$ will be

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Important Questions on Properties of Solids and Liquids

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

The decrease in length of a metal bar of length

L

and cross-sectional area

A

when compressed with a load

M

along its length is (

Y =

Young's modulus of the material of metal bar)

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

The value of

\tan θ

in the graph gives

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

The bulk modulus of a spherical object is

B

. If it is subjected to uniform pressure

p

, the fractional decrease in radius is

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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

]

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

A thin

1 m

long rod has a radius of

5 mm

. A force of

50 {π×10}^{3} N

is applied at one end to determine its Young's modulus. Assume that the force is exactly known. If the least count in the measurement of all lengths is

0.01 mm

, which of the following statements is false?

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

A steel wire of diameter

0.5 mm

and Young's modulus

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

carries a load of mass

M

. The length of the wire with the load is

1.0 m

. A vernier scale with

10

divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count

1.0 mm

, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by

1.2 kg

, the vernier scale division which coincides with a main scale division is __________. Take

g = 10 m s^{- 2} and π = 3.2

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

Two wires are made of the same material and have the same volume. The first wire has cross-sectional area

A

and the second wire has cross-sectional area

3 A .

If the length of the first wire is increased by

∆ l

on applying a force

F,

how much force is needed to stretch the second wire by the same amount?

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

A uniformly tapering conical wire is made from a material of Young's modulus

Y

and has a normal, unextended length

L

. The radii, at the upper and lower ends of this conical wire, have values

R

and

3 R

, respectively. The upper end of the wire is fixed to a rigid support and a mass

M

is suspended from its lower end. The equilibrium extended length, of this wire, would equal:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

A bottle has an opening of radius

a

and length

b

. A cork of length

b

and radius

(a + ∆ a)

where

(∆ a ≪ a)

, is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is

B

and the coefficient of friction between the bottle and cork is

μ

, then the force needed to push the cork into the bottle is

Question Image

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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?

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

Young's moduli of two wires

A

and

B

are in the ratio

7 : 4

. Wire

A

2 m

long and has radius

R .

Wire

B

1.5 m

long and has radius

2 m m .

If the two wires stretch by the same length for a given load, the value of

R

is close to:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

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:

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to

T_{M}

. If the Young's modulus of the material of the wire is

Y

, then

\frac{1}{Y}

is equal to:
(

g =

gravitational acceleration)

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Physics>Physical and Thermal Properties of Bulk Matter>Properties of Solids and Liquids>Stress Strain Relationship

The length of elastic string obeying Hooke's law is

l_{1}

metres when the tension is

4 N

and

l_{2}

metres when the tension is

5 N

. The length in metres when the tension is

9 N

is,

If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient η, the Poisson's ratio σ will be

Important Questions on Properties of Solids and Liquids

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If Young's modulus of elasticity Y for a material is one and half times its rigidity coefficient $η,$ the Poisson's ratio $σ$ will be