### Elasticity

Single Option Questions
1. An Indian rubber cord L metre long and area of cross-section A metre2 is suspended vertically. Density of rubber is D kg / metre3 and Young's modulus of rubber is E newton / metre2 . If the wire extends by l metre under its own weight, then extension l is
Ans: L2Dg / 2E
2. To break a wire, a force of 106 N / m2 is required. If the density of the material is 3 × 103 kg / m3, then the length of the wire which will break by its own weight will be
Ans: 34 m
Sol: 3. Two rods of different materials having coefficients of linear expansion α1, α2 and Young's moduli Y1 and Y2 respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If
α1 : α2 = 2 : 3, the thermal stresses developed in the two rods are equally provided Y1 : Y2 is equal to
Ans: 3 : 2
Sol: Thermal stress = YαΔ α.
If thermal stress and rise in temperature are equal then 4. The extension in a string obeying Hooke's law is x. The speed of sound in the stretched string is v. If the extension in the string is increased to 1.5x, the speed of sound will be
Ans: 1.22 v
Sol: 5. One end of a uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W1 is suspended from its lower end. If S is the area of cross-section of the wire, the stress in the wire at a height 3L/4 from its lower end is
Ans:  6. There are two wires of same material and same length while the diameter of second wire is 2 times the diameter of first wire, then ratio of extension produced in the wires by applying same load will be
Ans: 4 : 1 7. A particle of mass m is under the influence of a force F which varies with the displacement x according to the relation F = −kx + F0 in which k and F0 are constants. The particle when disturbed will oscillate
Ans:  8. An elastic material of Young's modulus Y is subjected to a stress S. The elastic energy stored per unit volume of the material is
Ans: 9. Two wires A and B of same length, same area of cross-section having the, same Young's modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is 3/2 times of that of wire B. The ratio of the forces produced in two wires will be
Ans: 3/2 10. A wire of area of cross-section 10−6 m2 is increased in length by 0.1%. The tension produced is 1000 N. The Young's modulus of wire is
Ans: 1012 N / m2 11. To break a wire of one meter length, minimum 40 kg wt. is required. Then the wire of the same material of double radius and 6 m length will require breaking weight
Ans: 160 kg-wt
Sol: Breaking force = Breaking stress × Area of cross section of wire
Breaking force ∝ r2 (Breaking distance is constant) If radius becomes doubled then breaking force will become 4 times i.e. 40 × 4 = 160 kg wt
12. The breaking stress of a wire of length L and radius r is 5 kg - wt / m2. The wire of length 2l and radius 2r of the same material will have breaking stress in kg - wt/m2
Ans:
Sol: Breaking stress depends on the material of wire.
13. The increase in length on stretching a wire is 0.05%. If its Poisson's ratio is 0.4, then its diameter
Ans: Reduce by 0.02% 14. If Poission's ratio σ is for a material, then the material is
Ans: Uncompressible 15. If the breaking force for a given wire is F, then the breaking force of two wires of same magnitude will be
Ans: 2F
Sol:  Breaking force ∝ Area of cross section
If area is double then breaking force will become two times.
16. If the thickness of the wire is doubled, then the breaking force in the above question will be
Ans: 4F
Sol: Breaking force ∝ r2
If thickness (radius) of wire is doubled then breaking force will become four times.

17. On all the six surfaces of a unit cube, equal tensile force of F is applied. The increase in length of each side will be (Y = Young's modulus, σ = Poission's ratio)
Ans:  18. The mass and length of a wire are M and L respectively. The density of the material of the wire is d. On applying the force F on the wire, the increase in length is l, then the Young's modulus of the material of the wire will be
Ans:  19. Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5 cm, the elongation (l) of each wire is
Ys (steel) = 2.0 × 1011  N / m2
Yc (copper) = 1.2 × 1011  N / m2
Ans: ls = 0.75 cm, lc = 1.25 cm 20. If the compressibility of water is σ per unit atmospheric pressure, then the decrease in volume V due to P atmospheric pressure will be
Ans: σ PV 21. A rectangular block of size 10cm × 8cm × 5cm is kept in three different positions P, Q and R in turn as shown in the figure. In each case, the shaded area is rigidly fixed and a definite force F is applied tangentially to the opposite face to deform the block. The displacement of the upper face will be Ans: Maximum in R position For maximum displacement area at which force applied should be minimum and vertical side should be maximum, this is given in the R position of rectangular block.

Graphical Questions
22.
The graph shown was obtained from experimental measurements of the period of oscillations T for different masses M placed in the scale pan on the lower end of the spring balance. The most likely reason for the line not passing through the origin is that the Ans: Mass of the pan was neglected If we draw a graph between T2 and M then it will be straight line.
and for M = 0, T2 = 0
i.e. the graph should pass through the origin.
but from the it is not reflected it means the mass of pan was neglected.

23. A graph is shown between stress and strain for a metal. The part in which Hooke's law holds good is Ans: OA 24. In the graph, point B indicates
Ans: Yield point

25. In the graph, point D indicates
Ans: Breaking point

26. The strain-stress curves of three wires of different materials are shown in the figure. P, Q and R are the elastic limits of the wires. The figure shows that
a) Elasticity of  wire P is maximum       b) Elasticity of  wire Q is maximum
c) Tensile strength of R is maximum    d) None of the above is true Ans: None of the above is true 27. The diagram shows a force-extension graph for a rubber band. Consider the following statements I. It will be easier to compress this rubber than expand it
II. Rubber does not return to its original length after it is stretched
III. The rubber band will get heated if it is stretched and released
Which of these can be deduced from the graph
Ans: III only
Sol: Area of hysterisis loop gives the energy loss in the process of stretching and unstretching of rubber band and this loss will appear in the form of heating.

28. The stress versus strain graphs for wires of two materials A and B are as shown in the figure. If  YA and YB are the Young ‘s modulii of the materials, then Ans: YA = 3YB 29. The load versus elongation graph for four wires of the same material is shown in the figure. The thickest wire is represented by the line Ans: OD i.e. for the same load, thickest wire will show minimum elongation. So graph D represent the thickest wire.

30. The adjacent graph shows the extension (l) of a wire of length 1m suspended from the top of a roof at one end with a load W connected to the other end. If the cross sectional area of the wire is 10-6 m2, calculate the young’s modulus of the material of the wire Ans: 2 × 1011 N / m2 31. The graph is drawn between the applied force F and the strain (x) for a thin uniform wire. The wire behaves as a liquid in the part Ans: bc
Sol: At point b, yielding of material starts.

32. The graph shows the behaviour of a length of wire in the region for which the substance obeys Hook’s law. P and Q represent Ans: P = extension, Q = stored elastic energy
Sol: Graph between applied force and extension will be straight line because in elastic range, Applied force µ extension but the graph between extension and stored elastic energy will be parabolic in nature 33. The potential energy U between two molecules as a function of the distance X between them has been shown in the figure. The two molecules are Ans: Attracted when x lies between B and C and are repelled when X lies between A and B
Sol: In the region BC slope of the graph is positive
... F = negative i.e. force is attractive in nature
In the region AB slope of the graph is negative
... F = positive i.e. force is repulsive in nature

34. The value of force constant between the applied elastic force F and displacement will be Ans:  35. The diagram shows stress v/s strain curve for the materials A and B. From the curves we infer that Ans: A is ductile and B is brittle
Sol: In ductile materials, yield point exist while in Brittle material, failure would occur without yielding.

36. Which one of the following is the Young’s modulus (in N/m2) for the wire having the stress-strain curve shown in the figure Ans: 2.0 × 1011 37. The diagram shows the change x in the length of a thin uniform wire caused by the application of stress F at two different temperatures T1 and T2. The variations shown suggest that Ans: T1 > T2

Sol: Elasticity of wire decreases at high temperature i.e. at higher temperature slope of graph will be less.
So we can say that T1 > T2

38. A student plots a graph from his reading on the determination of Young’s modulus of a metal wire but forgets to label.  The quantities on X and Y axes may be respectively. Ans: Stress applied and strain developed

39. The points of maximum and minimum attraction in the curve between potential energy (U) and distance (r)of a diatomic molecules are respectively Ans: S and T

Sol: Attraction will be minimum when the distance between the molecule is maximum.
Attraction will be maximum at that point where the positive slope is maximum because 40. The stress-strain curves for brass, steel and rubber are shown in the figure. The lines A, B and C are for Ans: Steel, brass and rubber respectively Assertion & Reason
Read the assertion and reason carefully to mark the correct option out of the options given below:
(a) If both assertion and reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion and reason are true but reason is not the correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If the assertion and reason both are false.
(e) If assertion is false but reason is true.

41. Assertion: The stretching of a coil is determined by its shear modulus.
Reason: Shear modulus change only shape of a body keeping its dimensions unchanged.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol: Because, the stretching of coil simply changes its shape without any change in the length of the wire used in coil. Due to which shear modulus of elasticity is involved.

42. Assertion: Spring balances show correct readings even after they had been used for a long time interval.
Reason: On using for long time, spring balances losses its elastic strength.
Ans: Assertion is false but reason is true.
Sol: When a spring balance has been used for a long time, the spring in the balance fatigued and there is loss of strength of the spring. In such a case, the extension in the spring is more for a given load and hence the balance gives wrong readings.

43. Assertion: Steel is more elastic than rubber.
Reason: Under given deforming force, steel is deformed less than rubber.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol: Elasticity is a measure of tendency of the body to regain its original configuration. As steel is deformed less than rubber therefore steel is more elastic than rubber.

44. Assertion: Glassy solids have sharp melting point.
Reason: The bonds between the atoms of glassy solids get broken at the same temperature.
Ans: The assertion and reason both are false.

Sol: In a glassy solid (i.e., amorphous solid) the various bonds between the atoms or ions or molecules of a solid are not equally strong. Different bonds are broken at different temperatures. Hence there is no sharp melting point for a glassy solid.

45. Assertion: A hollow shaft is found to be stronger than a solid shaft made of same material.
Reason: The torque required to produce a given twist in hollow cylinder is greater than that required to twist a solid cylinder of same size and material.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.

46. Assertion: Bulk modulus of elasticity (K) represents incompressibility of the material.
Reason: Bulk modulus of elasticity is proportional to change in pressure.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol: Bulk modulus of elasticity measures how good the body is to regain its original volume on being compressed. Therefore, it represents incompressibility of the material. where P is increase in pressure, V is change in volume.

47. Assertion: Strain is a unitless quantity.
Reason: Strain is equivalent to force.
Ans: Assertion is true but reason is false.

Sol: Strain is the ratio of change in dimensions of the body to the original dimensions. Because this is a ratio, therefore it is dimensionless quantity.

48. Assertion: The bridges declared unsafe after a long use.
Reason: Elastic strength of bridges losses with time.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion.
Sol: A bridge during its use undergoes alternating strains for a large number of times each day, depending upon the movement of vehicles on it when a bridge is used for long time, it losses its elastic strength. Due to which the amount of strain in the bridge for a given stress will become large and ultimately, the bridge may collapse. This may not happen, if the bridges are declared unsafe after long use.

49. Assertion: Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Both the balls will rise to same height after bouncing.
Reason: Ivory and wet-clay have same elasticity.
Ans: The assertion and reason both are false.
Sol: Ivory is more elastic than wet-clay. Hence the ball of ivory will rise to a greater height. In fact the ball of wet-clay will not rise at all, it will be somewhat flattened permanently.

50. Assertion: Young’s modulus for a perfectly plastic body is zero.
Reason: For a perfectly plastic body, restoring force is zero.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion. 51. Assertion: Identical springs of steel and copper are equally stretched. More work will be done on the steel spring.
Reason: Steel is more elastic than copper.
Ans: Both assertion and reason are true and the reason is the correct explanation of the assertion. Since, elasticity of steel is more than copper, hence more work has to be done in order to stretch the steel.

52. Assertion: Sterss is the internal force per unit area of a body.
Reason: Rubber is less elastic than steel.
Ans: Both assertion and reason are true but reason is not the correct explanation of the assertion.
Sol: Stress is defined as internal force (restoring force) per unit area of a body. Also, rubber is less elastic than steel, because restoring force is less for rubber than steel.

Posted Date : 17-02-2021

గమనిక : ప్రతిభ.ఈనాడు.నెట్లో వచ్చే ప్రకటనలు అనేక దేశాల నుండి, వ్యాపారస్తులు లేదా వ్యక్తుల నుండి వివిధ పద్ధతులలో సేకరించబడతాయి. ఆయా ప్రకటనకర్తల ఉత్పత్తులు లేదా సేవల గురించి ఈనాడు యాజమాన్యానికీ, ఉద్యోగస్తులకూ ఎటువంటి అవగాహనా ఉండదు. కొన్ని ప్రకటనలు పాఠకుల అభిరుచిననుసరించి కృత్రిమ మేధస్సు సాంకేతికతతో పంపబడతాయి. ఏ ప్రకటనని అయినా పాఠకులు తగినంత జాగ్రత్త వహించి, ఉత్పత్తులు లేదా సేవల గురించి తగిన విచారణ చేసి, తగిన జాగ్రత్తలు తీసుకొని కొనుగోలు చేయాలి. ఉత్పత్తులు / సేవలపై ఈనాడు యాజమాన్యానికి ఎటువంటి నియంత్రణ ఉండదు. కనుక ఉత్పత్తులు లేదా సేవల నాణ్యత లేదా లోపాల విషయంలో ఈనాడు యాజమాన్యం ఎటువంటి బాధ్యత వహించదు. ఈ విషయంలో ఎటువంటి ఉత్తర ప్రత్యుత్తరాలకీ తావు లేదు. ఫిర్యాదులు తీసుకోబడవు.