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Kristina Dorsey
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1 Easticity. The strain produced in the stretched spring is ) Voume Strain ) Shearing Strain 3) Tensie Strain 4) None of the above. A body subjected to strain a number of times does not obey Hooke's aw due to ) Yied point ) Breaking stress 3) Eastic fatigue 4) Permanent set 3. The moduus of easticity is dimensionay equivaent to ) Stress ) Surface Tension 3) Strain 4) Coefficient of Viscosity 4. Which of the foowing substances has the highest easticity? ) Rubber ) Stee 3) Copper 4) Wood 5. In the given figure if the dimension of the wires are the same and materias are different Young's moduus is ess for ) A ) B 3) Both 4) None 6. A heavy mass is attached to a thin wire and is whired in a vertica circe. The wire is most ikey to break ) When the mass is at the owest point. ) When mass is at the highest point. 3) When wire is horizonta. 4) When mass is at an ange of cos from upward vertica.

2 7. Stee is preferred for making springs over copper because ) Young's moduus of stee is more than that of copper. ) Stee is cheaper. 3) Young's moduus of copper is more. 4) Stee is ess ikey to be oxidized. 8. The possibe vaue of Poisson s ratio is ) 0.9 ) 0.8 3) 0.4 4) 9. The breaking stress of a wire depends on ) Materia of a wire ) Shape of cross section 3) Length of the wire 4) Radius of the wire 0. The property of metas whereby they coud be drawn into thin wires beyond their eastic imit without breaking is ) Ductiity ) Maeabiity 3) Easticity 4) Hardness. When an eastic materia with young's moduus 'y' is subjected to a stretching stress 'S' the eastic energy stored per unit voume of the materia is --- ) YS ) S Y. A wire of ength 'L' and cross sectiona area 'A' is made up of a materia of young's moduus 'Y'. If the wire is stretched by 'X' the work done is ) YAX L ) YAX 3) S Y 3) YAX 4) 3. The formua for strain energy per unit voume a) / (stress)(strain) b) / Y (strain) c) x y (stress) d) x (strain) Y ) a, b are correct ) a, c are correct 3) c, d are correct 4) a, b, c are correct 4. Four springs of force constants K =000N/m, K =500 N/m, K 3 =500 N/m and K 4 =000 N/m are subjected to different oads producing same extension. Arrange the springs with work done in descending order ),,3,4 ) 3, 4,, 3) 3,,, 4 4) 3, 4,, 4) S Y YAX L

3 5. Consider the statements A and B and identify the correct answer given beow. A) If the voume of a body remains unchanged, when subjected to tensie strain, the vaue of Poisson s ratio is / B) Phosphor bronze has ow Young's moduus and high rigidity moduus ) A and B are correct ) A and B are wrong 3) A is correct and B is wrong 4) A is wrong and B is right 6. The breaking stress of wire depends upon ) Length of wire ) Radius of wire 3) Materia of wire 4) Shape of cross section 7. Which of the foowing affects the easticity of a substance? ) Hammering and anneaing ) Change in temperature 3) Impurity in substance 4) A of these 8. Consider an idea mono-atomic gas of voume at pressure P. The buk moduus at constant temperature is ) p ) P 3) γ P 4) PdP dv 9. The foowing four wires are made of the same materia subjected to same force arrange them with their eongations in ascending order a) = 50cm and r = 0.5mm b) = 00cm and r = mm c) = 00cm and r = mm d) = 300cm and r = 3mm () a, b, c, d () c, d, a, b (3) a, d, c, b (4) d, c, b, a 0. (A): Young s moduus for a perfecty pastic body is zero. (R): For a perfecty pastic body, restoring force is zero. () Both (A) and (R) are true and (R) is the correct expanation of (A). () Both (A) and (R) are true and (R) is not the correct expanation of (A). (3) (A) is true but (R) is fase. (4) (A) is fase but (R) is true.. (A): Identica springs of stee and copper are equay stretched. More work wi be done on the stee spring. (R): Stee is more eastic than copper. () Both (A) and (R) are true and (R) is the correct expanation of (A). () Both (A) and (R) are true and (R) is not the correct expanation of (A). (3) (A) is true but (R) is fase.

4 (4) (A) is fase but (R) is true.. Assertion (A): Ductie metas are used to prepare thin wires. Reason (R): In the stress-strain curve of ductie metas, the ength between the points representing eastic imit and breaking point is very sma. ) Both (A) and (R) are true and (R) is the correct expanation of (A). ) Both (A) and (R) are true and (R) is not correct expanation of (A). 3) (A) is true but (R) is fase. 4) (A) is fase but (R) is true. 3. Match the foowing. List I (a) Spring constant (b) Tensie strength (c) Buk moduus List II (e) (f) ( stress) Y p V / V (g) Breaking stress (d) Potentia energy/ Unit voume (h) AY L () a-h, b-g, c-f, d-e () a-g, b-h, c-e, d-f (3) a-e, b-h, c-f, d-g (4) a-h, b-e, c-f, d-g 4. Match the ist I with List II. List I (a) Anneaing (b) Compressibiity (c) Tensie strength (d) Work hardening List II (e) Increasing the strength of a soid (f) Maximum stress for which an object may not break (g) Sow cooing after heating (h) Reciproca of Buk moduus () a-e, b-g, c-f, d-h () a-e, b-f, c-g, d-h (3) a-g, b-f, c-h, d-e (4) a-g, b-h, c-f, d-e 5. Consider the statements A and B, identify the correct answer given beow: (A): If the voume of a body remains unchanged when subjected to tensie strain, the vaue of Poisson s ratio is /. (B): Phosphor bronze has ow Young's moduus and high rigidity moduus. ) A and B are correct ) A and B are wrong 3) A is correct and B is wrong 4) A is wrong and B is right

5 6. Which of the foowing reations is not correct Y = young's moduus, K = buk moduus, n= rigidity moduus, σ = poisons ratio ) /Y = 9 η K/(3K +η ) ) Y/ η = ( +σ ) 3) Y/3 K = ( -σ ) 4) (Y/η ) +(Y/3K)=3 7. a) A wire is stiffer if Y is arge. b) A wire is stiffer if Y is sma. c) A wire is stronger if the breaking stress is arge. d) A wire is stronger if the breaking stress is sma. ) b, c ) b, d 3) a, d 4) a, c 8. a) Spring constant is directy proportiona to the ength of the wire. b) The spring constant is directy proportiona to the cross sectiona area of the wire. c) The spring constant is inversey proportiona to the ength of the wire. d) The spring constant is inversey proportiona to the cross sectiona area of the wire. ) b, c ) a, b 3) a, d 4) c, d 9. When a very ong rod suspended in air wi break under its own weight. The maximum ength of the rod wi depend on a) Breaking stress b) Density c) Cross sectiona ` d) Acceeration due to gravity ) a, b, c ) a, b, d 3) b, c, d 4) a, b, c, d 30. Identify the correct statements. a) Each time an object is subjected to stress; its interna structure undergoes change in the course of time. b) Poisson s ratio is a moduus of easticity. c) Rigidity moduus is reevant for both soids and iquids. d) The strength of a materia can be improved by incorporating for eign atoms. ) a, b ) a, c 3) a, d 4) b, c 3. When a wire is stretched to doube its ength? a) Stress = Young s moduus b) Strain = c) Radius is haved d) Y = x eastic deformation energy

6 ) a, b, c ) b, c, d 3) a, c, d 4) a, b, d 3. Arrange the foowing materias in the increasing order of easticity. a) Stee b) Lead c) Rubber d) Gass ) c, b, d, a ) a, b, c, d 3) a, d, b, c 4) b, d, a, c 33. Arrange the eastic moduii, stretch moduus (Y), shear moduus (n) and buk moduus (K), in the decreasing order for typica materias. ) Y, n, K ) Y, K, n 3) K, Y, n 4) n, K, Y 34. Arrange the foowing parameters for easticity, yied point (Y), Limit of proportionaity (P), range of Hooke s aw (H) and Breaking stress (B)., in the increasing order of stress. ) B, Y, P, H ) H, Y, P, B 3) H, P, Y, B 4) H, Y, B, P 35. Arrange the compressibiity of the iquids Mercury (M) Ethy acoho (E). Gycerin (G), and Water (W), in the decreasing order. ) E, W, G, M ) M, G, W, E 3) E, G, W, M 4) M, W, G, E 36. Match the foowing. List I List II a) Pastic deformation e) Faiure of an object after repeated appication of stresses that are we under its origina breaking strength b) Eastic fatigue f) Maximum stress that can appied to an object without its being permanenty deformed c) Eastic Limit g) Abiity to deform a great dea beyond the eastic imit d) Ductiity h) When the eastic imit is exceeded and the tension is removed, the rod remains onger than it was originay ) a g, b h, c e, d f ) a f, b h, c g, d e 3) a h, b e, c f, d g 4) a h, b f, c e, d g 37. Match the foowing. List I List II a) Anneaing e) Increasing the strength of a soid b) Compressibiity f) Maximum stress for which an object may not break c) Tensie strength g) Sow cooing after heating d) Work hardening h) Reciproca of Buk moduus

7 ) a e, b g, c f, d h ) a e, b f, c g, d h 3) a g, b f, c h, d e 4) a g, b h, c f, d e 38. Assertion (A): A wire may be stiffer than another wire B. But B may stronger than A. Reason (R): A high young s moduus does not necessariy impy a high vaue for the breaking stress. ) Both A and R are true, and R is the correct expanation of A. ) Both A and R are true, but R is not the correct expanation of A. 3) A is true but R is fase. 4) R is true but R is fase. 39. Assertion (A): To increase the strength of a soid, it is necessary to impede the motion of disocation sin its structure. One way is to increase the number of disocations by hammering the meta or squeezing it between roers. Reason (R): The disocations then become so numerous and tanged together that they interfere with each other s motion. ) Both A and R are true, and R is the correct expanation of A. ) Both A and R are true, but R is not the correct expanation of A. 3) A is true but R is fase. 4) R is true but R is fase. 40. Assertion (A): A hippopotamus has thicker egs for its size than a mouse does. Reason (R): The compressive oad on the eg bones of an anima depends on its weight, which in turn varies as the cube L 3 of a representative inear dimension L such as its ength or height. The strength of a bone, however, depends on its cross sectiona area which for simiar animas varies as L. A arge anima must have reativey thicker eg bones than a sma one because L 3 increases faster than L ) Both A and R are true, and R is the correct expanation of A. ) Both A and R are true, but R is not the correct expanation of A. 3) A is true but R is fase. 4) R is true but R is fase.

8 4. The area of cross-section of a wire is 0 5 m when its ength is increased by 0.% a tension of 000N is produced. The Young's moduus of the wire wi be ---- ) 0 Nm ) 0 Nm 3) 0 9 Nm 4) 0 0 Nm 4. The foowing four wires are made of the same materia. Which of these wi have the argest eongation when the same tension is appied? ) = 50cm and diameter 0.5mm ) = 00cm and diameter.0mm 3) = 00cm and diameter.0mm 4) = 300cm and diameter 3.0mm 43. If stress is numericay equa to young's moduus the eongation wi be ) 4 the origina ength ) the origina ength 3) Equa to the origina ength 4) Twice the origina ength 44. A metaic ring of radius 'r' and cross sectiona area A is fitted into a wooden circuar disc of radius R (R > r). If the Young's moduus of the materia of the ring is Y, the force with which the meta ring expands is ) AYR r ) AY ( R r) r 3) Y( R r) Ar 4) YR AR 45. When the tension on a wire is 4N its ength is. When the tension on the wire is 5N its ength is. Find its natura ength. ) 5 4 ) 4 5 3) 0 8 4) When a tension 'F' is appied, the eongation produced in uniform wire of ength, radius r is e, when tension F is appied, the eongation produced in another uniform wire of ength and radius r made of same materia is ) 0.5e ).0e 3).5e 4).0e 47. Two bars A and B of circuar cross section and of same voume made of same materia are subjected to tension. If the diameter of A is haf that of B and if the force appied to both the rods is the same and it is in the eastic imit the ratio of extension of A to that of B wi be ) 6 ) 8 3) 4 4)

9 48. Two wires of same ength and thickness are joined end to end. Their Young's moduii are 5x0 0 pa and 0x0 0 pa. If the combination is stretched by a certain oad, the eongations of these wires wi be in the ratio ) 3:4 ) 4:3 3) : 4) : 49. Two rods of different materias having coefficients of inear expansion α and α and Young s moduii Y and Y respectivey are fixed between two rigid massive was. The rods are heated such that they undergo the same increase in temp. There is no bending of rods. If α : α = :3. The therma stresses deveoped in the two rods are equa if Y : Y is equa to ) 4: 9 ) 3: 3) 9: 4 4) : 50. A cubica ba is taken to a depth of 00m in a sea. The decrease in voume observed to be 0.%. The buk moduus of the ba is -- (g = 0 ms - ) ) x0 7 Pa ) x0 6 Pa 3) x0 9 Pa 4).x0 9 Pa 5. The increase in ength of a wire on stretching is 0.05%. If its poisons ratio is 0.4, then the percentage decrease in the diameter is: ) 0.0 ) 0.0 3) ) The breaking stress of stee is 7.9x0 9 Nm and density of stee is 7.9x0 3 kgm 3 and g = 0ms. The maximum ength of stee wire that can hang verticay without breaking is ) 0 3 m ) 0 4 m 3) 0 m 4) 0 5 m 53. A meta cube of side ength 8.0 cm has its upper surface dispaced with respect to the bottom by 0.0 mm when a tangentia force of 4 x 0 9 N is appied at the top with bottom surface fixed. The rigidity moduus of the materia of the cube is ) 4 x 0 9 N/m ) 5 x 0 9 N/m 3) 8 x 0 9 N/m 4) x 0 8 N/m 54. A oad of kg weight is attached to one end of a stee wire of cross sectiona area 3 and Young s moduus 0 N/m. The other end is suspended verticay from a hook on a wa, and then the oad is pued horizontay and reeased. When the oad passes through its owest position the fractiona change in ength is (g=0m/s ) ) 0 4 )0 3 3) 0 3 4) 0 4

10 55. The radii and Young s moduus of two uniform wires A & B are in the ratio : and : respectivey. Both the wires are subjected to the same ongitudina force. If increase in the ength of wire A is %, then the percentage increase in ength of wire B is ) ).5 3) 4) A wire whose cross sectiona area is mm is stretched by 0. mm by a certain oad. If a simiar wire of tripe the area of cross section is stretched by the same oad, the eongation of the second wire woud be ) 0.33m ) 0.033mm 3) 0.3mm 4) mm 57. A wire eongates by mm when a oad W is hanged from it. If the wire goes over a puey and two weights W each are hung at the two ends, the eongation of the wire wi be (in mm) ) Zero ) / 3) 4) 58. The increase in pressure required to decrease the 00 iters voume of a iquid by 0.004% in k Pa is: (buk moduus of the iquid = 00 MPa) ) 8.4 ) 84 3) 9.4 4) A copper soid cube of 60mm side is subjected to a compressibe pressure of.5 x 0 7 Pa. If the buk moduus of copper is.5 x 0 Pasca, the change in the voume of cube is ) -43. mm 3 ) -43.m 3 3) -43. cm 3 4) -43 m m When a wire of ength 0m is subjected to a force of 00 N aong its ength, the atera strain produced is 0.0X 0-3. The Poisson s ratio was found to be 0.4. If the area of cross-section of wire is 0.05, its Young s moduus is ).6 x 0 8 N/m ).5 x 0 0 N/m 3).5 x 0 N/m 4)6 x 0 9 N/m

11 6. A stee wire of diameter d, area of cross-section A and ength is camped firmy at two points A and B which are m apart and in the same pane. A body of mass m is hung from the midde point of wire such that the midde point sags by x ower from origina position. If Young s moduus is Y then m is given by ) YAx g ) YA gx 6. A meta rod of Young's moduus 0 0 Nm - undergoes an eastic strain of 0.0% the energy per unit voume stored in the rod in joue/m 3 is ) 400 ) 800 3) 00 4) The work done in stretching a wire by mm is J. The work necessary for stretching another wire of same materia but with doube the radius of cross-section and haf the ength by mm is in Joues ) 6 ) 8 3) 4 4) ¼ 64. Two wires of same radius and ength are subjected to the same oad. One wire is of stee and the other is of copper. It the Young's moduus of stee is twice that of copper, the ratio of eastic energy stored per unit voume in stee to that of copper wire is ) : ) : 3) :4 4) 4: 65. A spring of force constant 800N/m has an extension of 5cm. The work done in extending it from 5cm to 5cm is 3) YAx 3 g ) 6J ) 8J 3) 3J 4) 4J 66. A hoow cyinder of inner radius 3 cm and outer radius 5 cm and a soid cyinder of radius cm are subjected to the same force. If they are made of same materia and of same ength, then the ratio of their eongations is ) : ) : 3) : 4 4) : 3 3 4) YA gx

12 67. The ength of a rubber cord is meters when the tension is 4N and meters when the the tension is 5N. The ength in meters when the tension is 9 N is ) 5-4 ) 5-4 3) 9-8 4) Two wires A & B are identica in shape and size and are stretched by same magnitude of force. Then the extensions are found to be 0.% and 0.3% respectivey. Find the ratio of their Young's moduii ) : 3 ) 3 : 3) 4 : 9 4) 9 : One end of a uniform wire of ength L and of weight W is attached rigidy to a point in the roof and a weight W is suspended from its ower end. If 'S' is the area of cross- section of the wire, then find the stress in the wire at height (3L/4) from its ower end? w + (3w/4) ) S w + (3w /4) ) S w + w 3) 4 3w + (w/4) 4) S 7. A ight rod of ength 00cm is suspended from the ceiing horizontay by means of two vertica wires of equa ength tied to its ends. One of the wires is made of stee and is of cross-section 0.sq.cm and the other is of brass of cross-section 0. sq.cm. Find the position aong the rod at which a weight may be hung to produce (i) equa stresses in both wires and (ii) equa strains in both wires. Y brass = 0x0 dyne/cm and Y stee = 0 x 0 dyne/cm ) 33.3cm; 00cm ) 67cm; 50cm 3) 00cm; 00cm 4) None 7. A ong stee wire of ength 'L' is suspended from the ceiing of a room. A sphere of mass 'm' and radius 'r ' is attached to the ower end of the wire. The height of the ceiing is (L+r +). When the sphere is made to osciate as a penduum, its owest point just touches the foor. The veocity of the sphere at the owest point wi be (L >> r, and r is the radius of the wire) ) π m r ye Lg ) π me r y Lg 3) π m y r e 4) None

13 73. A meta cube of side ength 8.0cm has its upper surface dispaced with respect to the bottom by 0.0 mm when tangentia force of 40 4 N is appied at the top with bottom surface fixed. The rigidity moduus of the materia of the cube is ) 40 9 Nm - ) 50 9 Nm - 3) 80 9 Nm - 4) 0 8 Nm A meta rope of density 6000kgm -3 has breaking stress 9.8x0 8 Nm. This rope is used to measure the depth of the sea. Then the depth of the sea that can be measured without breaking is ) 0x0 3 m ) 0x0 3 m 3) 30x0 3 m 4) 40x0 3 m 75. The upper end of a wire of radius 4mm and ength 00cm is camped and its other end is twisted through an ange of 30 0 then the ange of shear is ) ) ). 0 4) A uniform meta rod of mm cross section is heated from 0 0 C to 0 0 C. The coefficient of inear expansion of the rod is 0 6 /ºC. Its Young s moduus of easticity is 0 Nm. The energy stored per unit voume of the rod is ) 880 Jm 3 ) 500 Jm 3 3) 5760 Jm 3 4) 440 Jm Two springs of spring constants 500N/m and 3000 N/m respectivey are stretched by the same force. The potentia energy possessed by the two wi be in the ratio ) 4: ) :4 3) : 4) : 78. One end of a ong metaic wire of ength L is tied to the ceiing. The other end is tied to mass ess spring of spring constant K.A mass (m) hangs freey from the free end of the spring. The area of cross-section and Young s moduus of the wire are A and Y respectivey. If the mass is sighty pued down and reeased it wi osciate with a time period T equa to m ) π ) π k m( YA + KL) YAK mya ml 3) π 4) π KL YA 79. A mass m kg is whired in a vertica pane by tying it at the end of a fexibe wire of ength and area of cross section 'A'. When the mass is at its owest position the strain produced in the wire is, if Young s moduus of the wire is 'Y' (if V= 5g ) ) 6 AY mg ) 6mg AY 3) 5mg AY 4) 5 AY mg

14 80. On a the six surfaces of a unit cube, equa tensie force of F is appied. The increase in ength of each side wi be (Y = Young's moduus, σ = Poisson s ratio) ) F Y ( σ ) ) F Y ( + σ ) 3) F ( σ ) Y 4) F Y ( + σ ) Key ) ) 3 3) 4) 5) 6) 7) 8) 3 9) 0) ) 3 ) 4 3) 4) 4 5) 3 6) 3 7) 4 8) 9) 4 0) ) ) 3 3) 4) 4 5)3 6) 6) 7) 4 8) 9) 30) 3 3) 3 3) 33) 34).3 35) 36) 3 37) 4 38) 39) 40) 4) 4) 43) 3 44) 45) 46) 47) 48) 49) 50) 3 5) 5) 4 53) 54) 55) 3 56) 57)3 58) 59) 60) 6) 3 6) 63) 64) 65) 66) 3 67) 68) 69) 70) 7) 7) 73) 74) 75) 76) 77) 3 78) 79) 80) 3

15 Hints 4. 3 F 0 y = 0 N / m 5 3 e = 0 0 = A 0. = = F 4. e = e y( π r ) r (Same y and F) i.e. if r stress y = strain y y = strain Strain = = F = YA π ( R r) F = YA π r YA ( R r) F = r T 45. ( ) = Ay ( ) = () () is more, then extension is more T Ay T = T T T = T T e =

16 46. F y = Ae F = r e F r e e F r e = r F ( F)( ) r e = e 4r F =.0 e 47. e 4 A r e e A B re 6 = = = ra 4 B 4 A e y e = = = y e y F 49. F = y A ( t) = = y t A 50. y = const y α y y y α = α y = 3 PV ( hdg) V k = = V V k = = x 0 9 Pa 0./00 5. = 0.05% D 00 D / D σ = σ = D / 0V

17 0.4 = D 00 D D 00 = 0.0 D P. S = = dg = 0 5 m F 53. η = x A e 3mg = AY S r Y S r Y t B A A = t A B B 56. e α A 57. In both the cases, the tension in the wire remains the same. So, eongation wi be the same V P = K V PV V = K r r F 60. σ = ; Y = Ae 6. For equiibrium, mg = T sinθ Here sinθ = tanθ = x

18 YA YA, ( ) / T = = + x YAx From (i) YAx x mg = or YAx m = 3 g E stress strain V = E ( ) ( ) y strain V = strain = =.00 E v = = 4 x 0 E 400 Joue / m V = F W = ( strain)( voume) A F e = A A VAe W = F e W F r w r = W = 6 Joues E y V ( ) 3 r = 4r E V s ys y = = = E / V y y c c = 8 r W 65. W = k ( x x ) 800 [5 5] 0 4 = = 400 [00] x 0-4

19 W = 8 J 66. e r e = = r e r 5 3 = e e = = F Y = Ae = = A( ) A( ) A( x ) 4 4 = = 5 9 5x = x = 5x = (5 4 ) x = x = 5 x = 5-4 e r e r = x = e π = π () π e = π x y e = = = y e W w F + 4 stress = A s 7. Stress in stee = stress in brass T T T A A A T A 3 B s s s 0 = = = = 3 B s B B 0 s

20 T s x = T B ( - x) T T s B x = = x =.33m x stress T / A T / A strain = = y y y s s B B s B T T 3 A y ( 0 ) 0 = = = m = 00 cm 3 A y ( 0 0 ) s s s B B B mv 7. F = TB = + mg r yae y( π r ) e But F = = L L y( π r ) e mv = + mg L r y ( π r ) e = mv + mgl mv = y( π r ) e mg y( π r ) e V = g m y( π r ) e V = Lg m F F F 73. η = = = e e A. L. Le L L η = = 5 x 0 9 N/m Breaking stress own = = dg Lφ = rθ = φ = sheright ange θ = Twist ange r. θ φ = = L = Energy per unit voume = strees strain = ( ) Y α t = = 880 J/m 3

21 77. PE f. k spring = k e = F =const PE k 78. PE :PE = k : k = : K = k. ya L ya K + L YAk = YA + kl ( + kl) m YA T = π YAK 79. When mass is at owest position tension in wire = 6mg F 6mg Eongation = e = = AY AY F 80. Tensie strain on each face = Y Latera strain due to the other two forces acting on perpendicuar faces Tota increase in ength F = ( σ ) Y σf = Y

ELASTICITY PREVIOUS EAMCET QUESTIONS ENGINEERING

ELASTICITY PREVIOUS EAMCET QUESTIONS ENGINEERING. If the ratio of engths, radii and young s modui of stee and brass wires shown in the figure are a, b and c respectivey, the ratio between the increase