ELASTICITY PREVIOUS EAMCET QUESTIONS ENGINEERING

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1 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 in engths of brass and stee wires woud be: [009 E] ) ba c bc ) Ans : 4 e T L r y e T L r y Brass B B s s stee s S B B a 3) ba c 4). A mass of 6.5 kg is hanging from the end of a 60 cm ong stee wire (Y 0 Pa) with area of crosssection 0.05 cm. When it is revoving in a vertica circe it has an anguar veocity of revoutions per second, at the bottom of the circe. Approximate eongation of the wire (in meters) when the mass is at its owest point of the trajectory is (008 E) bc a ) ) ) ) Ans : Tension in the string on crossing the mean position mv mv T mg+ mg+ r ( ) V g cosθ But 0 θ 90 V g Given m T mg+ g 3mg e F Y Youngs moduus Ae L Ay When a wire of ength 0 m is subjected to a force of 00 N aong its ength, the atera strain produced is m. The poisson s ratio was found to be 0.4. If the area of cross-section of wire is 0.05 m, its young s moduus is (007 E) ).6 08 N/m ).5 00 N/m 3).5 0 N/m 4) 6 09 N/m

2 Easticity Ans : Poisson s ration Δr r atera strain σ Δ ongitudina strain Δ Δr r σ F F Y Ae e A y Nm 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. (006 E) ) 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) (A) is fase but (R) is true Ans : 3 Ductie metas can be drawn into thin wires. Therefore the ength between the points representing eastic imit and breaking point is arge 5. 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 increase in ength wire B is (005 E) ) ).5 3) 4) 3 Ans : 3 ra YA,, FA FB r Y B B

3 Easticity e A A ea from e A F e F F y e π A L Ae L Ay r y B LB r A y A e r A B yb LA e B LB 00 Percentage increase in ength of the wire B eb L A metaic ring of radius 'r' cross sectiona area 'A' is fitted in to a wooden circuar disk 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 : (M-004) ) Ans : AYR r ) AY ( R r) r Young s moduus of easticity y Ae yae Force L But e π R π r π R r [ ] 3) ( ) ( ) yaπ R r Ay R r F π r r B Y( R r) Ar 4) YR Ar Buk moduus of water is x 09 N/m. The pressure required to increase the density of water by 0.% in N/m is : (E-003) ) x 09 ) x 08 3) x06 4) x

4 Easticity Ans : 3 ΔV ΔV Given V V Buk stress p Buk strain Δ V Buk moduus (K) V ΔV P K 0 0 V Nm - 8. The Poisson's ratio of a materia is 0.4. If a force is appied to a wire of this materia, there is a decrease of cross-sectiona area by %. The percentage increase in its ength is : (E 00) Ans : ) 3% ).5% 3) % 4) 0.5% Δr Latera strain σ r ongitudina strain Δ Poisson s ration Given da A % but da dr dr % A r r d dr / r.5% σ The ength of an eastic string is 'a' metres when the ongitudina tension is 4N and 'b' meters when the ongitudina tension is 5N. The ength of the string in metres when the ongitudina tension is 9 N is ) a-b ) 5b-4a 3) b-(/4)a 4) 4a-3b (E-00) Ans : Let the origina ength of the string is, when the force is zero y F e From the reation Ae When the tension is 4N, then the ength is a 4 ( a )..() When the tention is 5N, then the ength is b 5 ( b )..() 4

5 Easticity Dividing () & () 4 a 5a 4b 5 b..(3) When the tension is 9N, then the ength is C 9 ( c )...(4) Dividing () & (4) 9 c 4 a 9a 9 4c 4 4c 9a 5 but 5a -4b 4c 9a 5a+ 0b 4c 0b 6a c 5b 4a 0. When a uniform wire of radius r is stretched by a kg weight, the increase in its ength is.00 mm. If the radius of the wire is r/ and other conditions remain in the same, increase in its ength is (E-000) ).00mm ) 4.00 mm 3) 6.00 mm 4) 8.00mm Ans : 4 From the reation y Ae π r e e r e r e r r / e r e 8mm MEDICAL. A ight rod of ength 00 cms is suspended from the ceiing horizontay by means of two vertica wires of equa engths tied to the ends of the rod. One of the wires is made of stee and is of area of cross - section 0.cm. The other wire is k of brass and of area of cross - section 0.cm. The position from the stee wire 5

6 Easticity aong the rod at which a oad is to be paced to produce equa stresses in both wires is : (Y stee 0 0 dynes/cm; Ybrass 00 dynes /cm) (009 M) ) 00/3cm )00/3 cm 3) 50cm 4) 75cm Ans : Given that stress in the wires is equa F F F 0. A A F 0. As the system is in equiibrium, taking moments about c F ( x ) F ( 00 x ) F 00 x F x Soving x 00 3 cm. When a wire is subjected to a force aong its ength, its ength increases by 0.4% and its radius decreases by 0.%. Then the Poisson s ratio of the materia of the wire is ) 0.8 ) 0.5 3) 0. 4) 0. Ans : Δr Latera strain σ r o ngitudina strain Δ Poisson s ration Two rods of different materias with coefficients of inear therma expansion α, α and Young s modui Y and Y respectivey are fixed between two rigid was. They are heated to have the same increase in temperature. If the rods do not bend and if α : α : 3, then the therma stresses deveoped in the two rods wi be equa when Y : Y is equa to (007 M) Ans : 3 ) : 3 ) : 5 3) 3 : 4) 5 : F y t Therma Stress A Δ As therma stress is equa 6

7 Easticity y α Δ t y α Δt y α y α y y 3 [ same rise in temperature] 4. A body subjected to strain severa times wi not obey Hook s aw due to (007 M) Ans: 3 ) Yied point ) permanent state 3) Eastic fatigue 4) Breaking stress Because of Eastic fatigue the body oses the property of easticity temporary. 5. A mass of 6.5 kg is hanging from the end of a 60 cm ong stee wire (Y 0 Pa) with area of crosssection 0.05 cm. When it is revoving in a vertica circe it has an anguar veocity of revoutions per second, at the bottom of the circe. Approximate eongation of the wire (in meters) when the mass is at its owest point of the trajectory is (006 M) Ans : ) ) ) ) y Youngs moduus Ae eongation ( e) Ay But e F mg+ mrω ( + ω ) mg mr L Ay Sub the given vaues e m 6. Two wires of same materia and same diameter have engths in the ratio :5. They are stretched by same force. The ratio of work done in stretching them is (005M) ) 5 : ) : 5 3) :3 4) 3 : Ans : Force congation Work done 7

8 Easticity But y e Ae Ay w F Ay Ay F L w [ since F,A, Y are same] w w 5 7. The increase in ength of a wire on stretching is 0.05%. If its Poisson's ratio is 0.4, then the percentage decrease in the diameter is : (004 M) Ans : ) 0.0 ) 0.0 3) ) 0.04 Poisson s ratio atera strain σ ongitudina strain atera strain σ ongitudina strain 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) : Phosper bronze has ow Young's moduus and high rigidity moduus. (M-003) ) 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 Ans : A is correct A) As V constant π r constant from sma approximation method Δr Δ + 0 r Δ Δr r 8

9 Easticity σ Poisson s ratio Δr r Δ Δr σ r Δr r A is correct B) Phosphor bronze has ow eongation hence high youngs moduus and ow rigidity moduus/ B is wrong 9. Two springs of force constants 000 N/m and 000 N/m are stretched by same force. The ratio of their respective potentia energies is : (M-00) Ans : ) : ) : 3) 4 : 4) : 4 Potentia energy F F Kx K K K PE. K PE PE : PE : K PE K A meta cube of side ength 8.0 cm has its uper surface dispaced with respect to the bottom by 0.0 mm when a tangentia force of 4 x 09 N is appied at the top with bottom surface fixed. The rigidity moduus of the materia of the cube is (00 M) ) 4 x 09 N/m ) 5 x 09 N/m 3) 8 x 09 N/m 4) x 08 N/m Ans : F / A η Rigidity moduus Strain Strain η N / m 9. When a tension F is appied, the eongation produced in uniform wire of ength 'L', radius 'r' is 'e'. When tension F is appied, the eongation produced in another uniform wire of ength 'L' and radius 'r' made of same materia is (000 M) 9

10 Easticity Ans : ) 0.5e ).0e 3).5e 4).0e We know e F L r e F L r e F 4r e F r e e e e 0

MECHANICAL ENGINEERING

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