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Question-1

Define the term elasticity.

Solution:
The property of a material body by virtue of which it regains its original configuration (i.e., shape and size) when the external deforming force is removed is called elasticity.

Question-2

What is elastic limit?

Solution:
Elastic limit is the maximum stress on removal of which, the body regains its original dimensions.

Question-3

A steel wire is stretched by a weight of 400N. If the radius of the wire is doubled, how will Young’s , modulus of the wire be affected?

Solution:
Young’s modulus of a material depends on the nature of the material and is independent of its dimensions. Therefore, y of a steel wire will not be affected due to the change of the radius of the wire.

Question-4

When a material is under tensile stress, the restoring forces are caused by inter atomic attraction, while under compressional stress, the restoring forces are due to inter atomic repulsion. Explain how?

Solution:
When a material is subjected to tensile stress, the distance between atoms becomes greater than their equilibrium separation. Because atoms try to come back to their equilibrium positions, restoring force is caused due to inter atomic attraction. On the other hand, when a compressional stress is applied, the distance between atoms becomes less than their equilibrium separation. Obviously, when atoms tend to acquire their equilibrium position, the restoring force is provided by inter atomic repulsion.

Question-5

Distinguish between elasticity and plasticity of materials.

Solution:
Elasticity: It is the property of the body due to which the body regains its original configuration (length, volume or shape) when the deforming forces are removed. The body which has this property is called an elastic body.

Plasticity: It is the property of the body due to which it does not regain to its original configuration (length, volume or shape) when the deforming forces are removed from it.

Question-6

What do you mean by ‘Elastic after effect’?

Solution:
Certain material bodies take some time to regain their original configuration when the deforming force is removed. The delay in regaining the original configuration by the bodies on the removal of the deforming force is called elastic after effect. The elastic after effect is negligibly small for quartz fiber and phosphor bronze. For this reason, the suspensions made from quartz and phosphor bronze are used in galvanometers and electrometers.

For glass fibre, elastic after effect is very large. It takes hours for glass fibre to return to its original state on the removal of the deforming force.

Question-7

The interatomic separation in a neutral H2 molecule is 0.74A and the binding energy is 4.75eV. If an electron of the molecule is removed, the resulting molecular ion H2+ has a binding energy of 2.8eV. Would you expect the separation between the two protons in H2+ to be greater or less than 9.74A?

Solution:
The separation between the two protons in H2+ would be greater than 0.74A. The experimental value is 1.06A.

Question-8

Why are atomic masses (on say the unified scale) not exact integers? Why is there a slight difference in the atomic mass of an element on different scales?

Solution:
Most of the elements have more than one isotope having different atomic masses e.g. chlorine has two isotopes 35cl, and 37cl.

Since the atomic mass of an element is the average relative mass of all natural isotopes of that element, these elements have fractional atomic masses.

There is a slight difference in the atomic mass of an element on different scales, because on the unified scale, we have chosen 1/12 mass of C-12 atom as a unit mass, as the mass of C-12 is exactly=1.0000amu. On the other hand, we have chose mass of hydrogen atom as unit, which is not exactly 1.0000amu. Due to this reason there is a slight difference in atomic mass of an element on different scales.

Question-9

A silica glass rod has a diameter of 1cm and is 10cm long. Estimate the largest mass that can be hung from it without breaking it.

Solution:
The ultimate strength of glass is 50 × 106Nm-2 . Therefore, the largest mass that can be hung from the glass rod is

=[(50 ×106Nm-2) × (πd2/4)]/g kg = 392.5kg.

Question-10

What will be the density of lead under a pressure of 20,000N/cm2 be? Density of lead is 0.80 ×1010N/m2.

Solution:
Bulk modulus, B=

= 0.80 x1019N/m2
= N/cm2

ΔP = 20,000N/cm2.

Question-11

Why are the bridges declared unsafe after long use?

Solution:
Due to the repeated stress and strain, the material used in the bridges loses elastic strength and ultimately may be collapsed. Hence bridges are declared unsafe after long use.

Question-12

What kind of elasticity is used in (a) suspension bridge (b) an automobile tyre (c) an automobile drive shaft (d) a coil spring (e) a water lift pump (f) rubber heels.

Solution:
(a) In a suspension bridge as there occurs a stretch in the ropes by the load of the bridge, the elasticity involved is linear or tensile.

(b) In an automobile tyre as air is compressed the elasticity involved in volume i.e., bulk

(c) In transmitting power an automobile shaft is sheared as it rotates so the elasticity involved to shear i.e., rigidity

(d) When coiled spring is stretched, the deformation of the wire of the spring is in the form of a twisting strain so the elasticity involved is shear i. e, rigidity.

(e) As in a water lift pump the water is compressed, the elasticity involved is shear i.e., bulk

(f) As the shape of rubber heel changes under stress, the elasticity involved is shear or rigidity.

Question-13

Why are girders I shaped?

Solution:
Girders support load at their ends. Neutral surfaces of the girder, lie in the middle. The filaments of the lower part suffers extension where as of upper part suffer compressions. Thus the end faces should be strong enough. Hence they are I shaped.

Question-14

Identical spring of steel and copper are equally stretched. On which more work will have to be done?

Solution:
Young’s modulus of steel is greater than of copper. Hence, in order to produce same extension large force will have to be applied on the steel spring than that on the copper spring. Obviously more work will be done on the steel spring.

Question-15

Why a spring balance does not give correct measurement, when it has been used for a long time?

Solution:
When a spring balance has been used for a long time, it develops an elastic fatigue, the spring of such a balance takes longer time to recover its original configuration and therefore it does not give correct measurement.

Question-16

What is the basis of deciding the thickness of metallic ropes used in cranes to lift the heavy weight?

Solution:
The thickness of metallic ropes used in cranes is decided on the basis of the elastic limit of the material of the rope and the factor of safety. Suppose in a crane the rope made of steel is used to lift a load up to 104 kg. Though we may not lift a load more than 10 kg but usually the rope is made for a factor of safety of 10, it should not break even when a load of 105 kg or a force of 105 ×9.8 is applied on it. If r is the radius of rope, then maximum stress= Now, the maximum stress must not exceed the breaking stress or even the elastic limit for steel. Since for steel, the elastic limit is 30×107Nm-2. Hence .

Now, the maximum stress must not exceed the breaking stress or even the elastic limit for steel. Since for steel, the elastic limit is 30×107Nm-2. Hence =20 ×107 r=33.2 cm In order to impart flexibility to the rope, it is made of a large number of wires twisted together.

Question-17

What is Young’s modulus of a substance? What are its units? How is it experimentally measured?

Solution:
Young's modulus: it is defined as the ratio of the linear stress to linear strain, provided the elastic limit is not exceeded. The unit of Y is Nm-2.

Determination of Young's modulus of the material of a wire:

The apparatus consists of two wires of the same length and equal thickness hung side by side from a rigid support as shown. The wire A (called the reference wire) carries a millimeter scale S and wire B (called the experimental wire) has a vernier scale V.

When the wire is loaded, that is, it is pulled down by a force, the reaction of the support provides an equal and opposite force. The experimental wire is initially loaded with some weight so as to make it straight and the reading of the vernier is recorded. The load is increased by say, 250g and the vernier reading is recorded again. The

Difference between two vernier readings gives the extension produced by the load.

If L is the initial length of the wire and M is the load required to produce an extension ΔL, then

Where r = radius of the wire


and r, the value of Y is

Knowing M, L, ΔL, and r, the value of Y is determined.

Question-18

A structural steel rod has a radius of 10mm and a length of 1m. A 100KN force F steches it along its length. Calculate

(a) the stress

(b) elongation

(c) strain on the rod

Given that the Young’s modulus, E of the structural steel is 2.0 × 1011 Nm-2.

Solution:

Where r = radius of the wire

Knowing M, L,ΔL and r, the value of Y is determined.

Question-19

Why any metallic part of machinery is never subjected to stress beyond the elastic limit of the material?

Solution:
A permanent deformation will be set in that metallic part of the machinery.

Question-20

The ratio stress/strain remains constant for small deformation. What will be the effect on this ratio when the deformation made is very large?

Solution:
When the deforming force is applied beyond elastic limit, the strain produced is more than that has been observed within elastic limit. Due to which the ratio stress/strain will decrease.

Question-21

A copper wire is stretched by 10N force. If the radius of the wire is decreased by 2%, how will the Young’s modulus of wire be affected?

Solution:
Since modulus depends only on the nature of the material, its value is not changed when its radius is decreased. Thus, Young’s modulus of the wire remains the same.

Question-22

The Young’s modulus of a wire of length L and radius r is Y. If the length is reduced to L/2 and radius r/2, what will be its Young’s modulus?

Solution:
The Young’s modulus remains the same as Y.

Question-23

A wire of length L and of area of cross section A is stretched through a certain length l. If Y is Young’s modulus of the material of the wire, what is the force constant of the wire?

Solution:

Question-24


Solution:
Consider two pieces of wires, one of steel and the other of rubber. Both the steel and rubber are of equal length 'L' and of equal area of cross-section 'a'. Let each be stretched by an equal force F. The change in length of the rubber wire (lr) is more than that of the steel (ls) i. e.,lr > ls. If ys and yr are the Young's moduli of steel and rubber respectively, then from the definition of Young's modulus.

Question-25

Why are the bridges declared unsafe after long use?

Solution:
Due to repeated stress and strain, the material used in the bridges loses elastic strength and ultimately it may collapse. Hence bridges are declared unsafe after long use.

Question-26

What kind of elasticity is used in (a) suspension bridge (b) an automobile tyre (c) an automobile drive shaft (d) a coil spring (e) a water lift pump (f) rubber heels?

Solution:
(a) In a suspension bridge, as there occurs a stretch in the ropes by the load of the bridge, the elasticity involved is linear or tensile.

(b) In an automobile tyre, as air is compressed the elasticity involved is volume, i.e., bulk.

(c) In transmitting power an automobile shaft is sheared as it rotates so the elasticity involved is shear i.e., rigidity.

(d) When coiled spring is stretched, the deformation of the wire of the spring is in the form of a twisting strain so the elasticity involved is shear i.e., rigidity.

(e) In a water lift pump, the water is compressed, hence the elasticity involved is volume, i.e., bulk.

(f) The shape of rubber heel changes under stress, hence the elasticity involved is shear or rigidity.

Question-27

A cable is shortened to half its original length. (a) How does it affect the elongation under a given load? (b) How does this affect the maximum load that it can support without exceeding the elastic limit?

Solution:
(a)

i.e., AL L

Hence when the original length of the cable becomes, L/2, Δ L i.e., elongation gets halved.

(b)

There is no change in the volume of the maximum load F as Δ L/L remains constant even on shorting the cable to half its original length (‘Y’ and ‘a’ remains the same for any length of the cable).

Question-28

Two wires of different materials are suspended from a rigid support. They have the same length and diameter and carry the same load at their free ends. (i) Will the stress and strain in each wire be the same? (ii) Will the extension in both wires be the same?

Solution:
(i) Stress in both the wires is the same as both the wires have the same diameter and carry the same load at their free ends. Strain will be different in the two wires as the wires are of different materials, even though the stress in the same.

(ii) The extension produced in both the wires are not the same because the original lengths of the two wires are equal and strains produced by them are different, hence the extension in the two wires will be different.




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