Tiêu đề 9. Mechanical Properties Of Solids.pdf ✅

1. Force constant of a spring (K) is synonymous to :- 2. Length of a spring of force constant k in its unscratched condition is l. The spring is cut into two parts which have their unscratched lengths in the ratio 1 2 l l q : :1 = . Force constants of the two parts k1 and k2 are then 3. A wire fixed at the upper end stretches by length by applying a force F. The work done in stretching is :- (1) 2 F (2) F (3) 2F (4) 2 F 4. A uniform rod of mass m, length L, area of cross-section A and Young's modulus Y hangs from the ceiling. Its elongation under its own weight will be 5. 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: (1) III only (2) II and III (3) I and III (4) I only 6. The length of a spring is  when a force of 4N is applied on it and the length is  when 5 N force is applied. Then the length of spring when 9 N force is applied is (1)5  – 4  (2)  –  (3) 5  – 4  (4) 9 (  –  ) 7. The pressure of a medium is changed from 1.01 × 105 Pa to 1.165 × 105 Pa to change its volume by 10% keeping the temperature constant. The bulk modulus of the medium is : (1) 204.8 × 105 Pa (2) 102.4 × 105 Pa (3) 15.5 × 105 Pa (4) 1.55 × 105 Pa 8 . Which of the following will be  if Y = 2.4  (1) –1 (2) 0. 2 (3) 0. 1 (4) –0.28 9. A car moves from X to Y with a uniform speed vu and returns to Y with a uniform speed vd. The average speed for this round trip is :- 10. The length of a rubber cord is 1 metre (when the tension is 4 N) and 2 metre (when the tension is 6 N) respectively. The length 3 (When the tension is 9 N) is :- (1) (2.5 2 – 1.5 1 ) m (2) (6 2 – 1.5 1 ) m (3) (3 1 – 2 2 ) m (4) (3.5 2 – 2.5 1 ) m 11. The mean distance between the atoms of iron is 3 × 10–10 m and inter atomic force constant for iron is 7 N/m. The Young's modulus of elasticity for iron is : Mechanical Properties of Solids
12. If 'S' is stress and 'Y' is Young's modulus of material of a wire, the energy stored in the wire per unit volume is :- 13. A wire of length L and cross-sectional area A is made of a material of Young's modulus Y. The work done in stretching the wire by an amount x is given by 14. 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 graphs is a straight line? 15. A rod is fixed between two points at 20°C. The coefficient of linear expansion of material of rod is 1.1  10–5 /°C and Young's modulus is 1.2  1011 N/m2 . Find the stress developed in the rod if temperature of rod becomes 10°C : (1) 1.32  107 N/m2 (2) 1.10  1015 N/m2 (3) 1.32  108 N/m2 (4) 1.10  106 N/m2 16. 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 modulus of the materials, then :- (1) YB = 2YA (2) YA = YB (3) YB = 3YA (4) YA = 3YB 17. The potential energy U between the atoms in a diatomic molecule as a function of the distance x between the atoms is shown in figure. The atoms (1) Attract each other when x is between A and B (2) Attract each other when x is between B and C (3) Attract each other when x is at B (4) Repel each other when x is at B 18. A wire of length l, area of cross-section A and Young's modulus of elasticity Y is suspended from the proof of a building. A block of mass m is attached at lower end of the wire. If the block is displacement from its mean position and then released the block starts oscillation. Time period of these oscillations will be :- (1) 2 Al mY  (2) 2 AY ml  (3) 2 ml YA  (4) 2 m YAl  19. A copper solid cube of 60 mm side is subjected to a pressure of 2.5 × 107 Pa. If the bulk modulus of copper is 1.25 × 1011N/m2 , the change in the volume of cube is -
(1) – 43.2 m3 (2) – 43.2 mm3 (3) – 43.2 cm3 (4) – 432 mm3 20. The length of a metal wire is 1 , when the tension in it is T1 and is 2 when the tension is T2. The unstretched length of the wire is :- (1) 1 2 (2) 1 2 2 (3) 1 2 2 1 2 1 T T T T − − (4) 1 2 2 1 2 1 T T T T + + 21. A wire can be broken by applying a load of 200 N. The force required to break another wire of the same length and same material, but double in diameter, is :- (1) 200 N (2) 400 N (3) 600 N (4) 800 N 22. The load versus elongation graph for four wires of the same material and same length is shown in the figure. The thinnest wire is represented by the line (1) OA (2) OB (3) OC (4) OD 23. When the temperature of a rod increases from t to t t + , Its moment of inertia increases from I to I I + . If  be the coefficient of linear expansion of the rod, then the value of I I  is:- (1) 2t (2) t (3) 2 t (4) t   24. A clock which keeps correct time at 20oC is subjected to 40oC. If coefficient of linear expansion of the pendulum is 12  10–6 per C, how much will it gain or lose in time? (1) 10.3 seconds/day (2) 20.6 seconds/day (3) 5 seconds/day (4) 20 minutes/day 25. A thin copper wire of length L increases in length by 1% when heated from 0oC to 100oC, If a thin copper plate of area 2L  L is heated from 0oC to 100oC, the percentage increase in its area will be (1) 1% (2) 2% (3) 3% (4) 4% 26. Two rods of different materials and identical cross sectional areas, are joined face to face at one end and their free ends are fixed to rigid walls. If the temperature of the surounding is increased by 30oC, The magnitude of the displacement of the joint of the rods is : (length of the rods, 1 2 = =1 unit, ratio of their Young's modulii, Y1/Y2 = 2; Coefficients of linear expansion are 1 and 2 ) (1) 5(  2 1 − ) (2) 10(  1 2 − ) (3) 10 2 (  2 1 − ) (4) 5(  1 2 − ) 27. A wire suspended vertically from one of its ends is stretched by attaching a weight of 200 N to the lower end. The weight stretches the wire by 1 mm. The elastic energy stored in the wire is :- (1) 0.1 J (2) 0.2 J (3) 10 J (4) 20 J
28. If the volume of a block of aluminium is decreased by 1%, the pressure (stress) on its surface is increased by : (Bulk modulus of Al = 7.5  1010 Nm–2 ) (1) 7.5  1010N-m–2 (2) 7.5  108N-m–2 (3) 7.5  106N-m–2 (4) 7.5  104N-m–2 29. A rectangular block is heated from 0°C to 100°C. The percentage increase in length is 0.10%. What will be the percentage increases in its volume? (1) 0.03% (2) 0.10% (3) 0.30% (4) None of these 30. A brass rod of length 500 mm and diameter 3mm is joined to a steel rod of same length and diameter at 50°C. If the coefficients of linear expansion of brass and steel are 2.5  10–5 °C–1 and 1.25  10– 5°C–1 , then change in length of the combined rod at 200°C is :- (1) 2.4 mm (2) 2.8 mm (3) 3.2 mm (4) 3.6 mm 31. One end of a long metallic wire of length L area of cross section A and Young’s modulus Y is tied to the ceiling. The other end is tied to a massless spring of force constant K. A mass m hangs freely from the free end of the spring. It is slightly pulled down and released. Its time period is given by- (1) 2 m K  (2) 2 mYA KL  (3) 2 mK YA  (4) ( ) 2 m KL YA KYA  + 32. A copper wire (Y= 1  1011 N/m2 ) of length 6m & a steel wire (Y=2  1011 N/m2 ) of length 4m each of cross section 10–5 m2 are fastened end to end & stretched by a tension of 100 N. The elongation produced in the copper wire is- (1) 0.2 mm (2) 0.4 mm (3) 0.6 mm (4) 0.8 mm 33. Young's modulus of elasticity of material depends upon (1) Nature of material (2)Force applied (3) Shape and size of body (4) All of these 34. Two wires of the same material have lengths in the ratio 1 : 2and their radii are in the ratio 1: 2 . If they are stretched by applying equal forces. The increase in their lengths will be in the ratio– (1) 2: 2 (2) 2 : 2 (3) 1 : 1 (4) 1 : 2 35. The Young's modulus of a wire is y. If the energy per unit volume is E, then the strain will be– (1) 2E y (2) E y 2 (3) Ey (4) E y 36. Compressibility per unit atm. pressure of water is '  ' and if due to pressure P there is decrement in volume V, find change is volume (1)  P / V (2)  PV (3)  / PV (4)  V / P 37. The following four wires of length L and radius 'r' are made of the same material. which of these will have the largest extension, when the same tension is applied :-