Title 09. Elasticity Easy.pdf ✅

1. The length of an iron wire is L and area of cross-section is A. The increase in length is l on applying the force F on its two ends. Which of the statement is correct (a) Increase in length is inversely proportional to its length L (b) Increase in length is proportional to area of cross-section A (c) Increase in length is inversely proportional to A (d) Increase in length is proportional to Young's modulus 2. The increase in length is l of a wire of length L by the longitudinal stress. Then the stress is proportional to (a) L/l (b) l/L (c) l L (d) 2 l L 3. The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum when the same tension is applied (a) Length 100 cm, Diameter 1 mm (b) Length 200 cm, Diameter 2 mm (c) Length 300 cm, Diameter 3 mm (d) Length 50 cm, Diameter 0.5 mm 4. The ratio of the lengths of two wires A and B of same material is 1 : 2 and the ratio of their diameter is 2 : 1. They are stretched by the same force, then the ratio of increase in length will be (a) 2 : 1 (b) 1 : 4 (c) 1 : 8 (d) 8 : 1 5. The Young's modulus of a wire of length L and radius r is Y N/m2 . If the length and radius are reduced to L/2 and r/2, then its Young's modulus will be (a) Y/2 (b) Y (c) 2Y (d) 4Y 6. A beam of metal supported at the two ends is loaded at the centre. The depression at the centre is proportional to (a) 2 Y (b) Y (c) 1/Y (d) 2 1/Y 7. When a certain weight is suspended from a long uniform wire, its length increases by one cm. If the same weight is suspended from another wire of the same material and length but having a diameter half of the first one then the increase in length will be (a) 0.5 cm (b) 2 cm (c) 4 cm (d) 8 cm 8. Hook's law defines (a) Stress (b) Strain (c) Modulus of elasticity (d) Elastic limit 9. A wire is loaded by 6 kg at its one end, the increase in length is 12 mm. If the radius of the wire is doubled and all other magnitudes are unchanged, then increase in length will be (a) 6 mm (b) 3 mm (c) 24 mm (d) 48 mm 10. The area of cross-section of a wire of length 1.1 metre is 1 mm2 . It is loaded with 1 kg. If Young's modulus of copper is 1.1 × 10 11N/m2 , then the increase in length will be (If g = 10m/s 2 ) (a) 0.01 mm (b) 0.075 mm (c) 0.1 mm (d) 0. 15 mm
11. On increasing the length by 0.5 mm in a steel wire of length 2 m and area of cross-section 2mm2 , the force required is [Y for steel= 2.2 × 10 11N/m2 ]] (a) 1.1 × 10 5N (b) 1.1 × 10 4N (c) 1.1 × 10 3N (d) 1.1 × 10 2N 12. If Young's modulus of iron is 2 × 10 11N/m2 and the interatomic spacing between two molecules is 3 × 10 −10metre, the interatomic force constant is (a) 60 N/m (b) 120 N/m (c) 30 N/m (d) 180 N/m 13. In CGS system, the Young's modulus of a steel wire is 2 × 10 12. To double the length of a wire of unit cross-section area, the force required is (a) 4 × 10 6dynes (b) 2 × 10 12dynes (c) 2 × 10 12newtons (d) 2 × 10 8dynes 14. The material which practically does not show elastic after effect is (a) Copper (b) Rubber (c) Steel (d) Quartz 15. If the temperature increases, the modulus of elasticity (a) Decreases (b) Increases (c) Remains constant (d) Becomes zero 16. A force F is needed to break a copper wire having radius R. The force needed to break a copper wire of radius 2R will be (a) F/2 (b) 2F (c) 4F (d) F/4 17. The relationship between Young's modulus Y, Bulk modulus K and modulus of rigidity  is (a) 9 3 K Y K   = + (b) 9 3 YK Y K + (c) 9 3 K Y K  = + (d) 3 9 K Y K   = + 18. The diameter of a brass rod is 4 mm and Young's modulus of brass is 9 × 10 10N/m2 . The force required to stretch by 0.1% of its length is (a) 360πN (b) 36 N (c) 144π × 10 3N (d) 36π × 10 5N 19. If x longitudinal strain is produced in a wire of Young's modulus y, then energy stored in the material of the wire per unit volume is (a) yx 2 (b) 2yx 2 (c) 1 2 y 2x (d) 1 2 yx 2 20. In a wire of length L, the increase in its length is l. If the length is reduced to half, the increase in its length will be (a) l (b) 2l (c) 2 l (d) None of the above 21. The Young's modulus of a rubber string 8 cm long and density 1.5kg/m3 is 5 × 10 8N/m2 , is suspended on the ceiling in a room. The increase in length due to its own weight will be (a) 9.6 × 10 −5m (b) 9.6 × 10 −11m
(c) 9.6 × 10 −3m (d) 9.6 m 22. A and B are two wires. The radius of A is twice that of B. They are stretched by the some load. Then the stress on B is (a) Equal to that on A (b) Four times that on A (c) Two times that on A (d) Half that on A 23. If the length of a wire is reduced to half, then it can hold the ......... load (a) Half (b) Same (c) Double (d) One fourth 24. To double the length of a iron wire having 0.5cm2 area of cross-section, the required force will be (Y = 10 12dyne/cm2 ) (a) 1.0 × 10 −7N (b) 1.0 × 10 7N (c) 0.5 × 10 −7N (d) 0.5 × 10 12dyne 25. The spring balance does not read properly after its long use, because (a) The elasticity of spring increases (b) The elasticity decreases (c) Its plastic power decreases (d) Its plastic power increases 26. Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is (a) Four times for wire A as for wire B (b)Twice for wire A as for wire B (c) Half for wire A as for wire B (d)One-fourth for wire A as for wire B 27. Why the spring is made up of steel in comparison of copper (a) Copper is more costly than steel (b)Copper is more elastic than steel (c) Steel is more elastic than copper (d)None of the above 28. Steel and copper wires of same length are stretched by the same weight one after the other. Young's modulus of steel and copper are 2 × 10 11N/m2 and 1.2 × 10 11N/m2 . The ratio of increase in length (a) 2 5 (b) 3 5 (c) 5 4 (d) 5 2 29. An area of cross-section of rubber string is 2cm2 . Its length is doubled when stretched with a linear force of 2 × 10 5dynes. The Young's modulus of the rubber in dyne/cm2 will be (a) 4 × 10 5 (b) 1 × 10 5 (c) 2 × 10 5 (d) 1 × 10 4 30. Increase in length of a wire is 1 mm when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be (a) 2 mm (b) 0.5 mm (c) 4 mm (d) 0.25 mm 31. The temperature of a wire of length 1 metre and area of cross-section 1cm2 is increased from 0°C to 100°C. If the rod is not allowed to increase in length, the force required will be (α = 10 −5/°C and Y = 10 11N/m2 ) (a) 10 3N (b) 10 4N (c) 10 5N (d) 10 9N 32. A rod of length l and area of cross-section A is heated from 0°C to 100°C. The rod is so placed that it is not allowed to increase in length, then the force developed is proportional to (a) l (b) 1 l −
(c) A (d) 1 A − 33. An aluminum rod (Young's modulus = 7 × 10 9N/m2 ) has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in order to support a load of 10 4Newton's is (a) 1 × 10 −2m2 (b) 1.4 × 10 −3m2 (c) 3.5 × 10 −3m2 (d) 7.1 × 10 −4m2 34. Two wires of copper having the length in the ratio 4 : 1 and their radii ratio as 1 : 4 are stretched by the same force. The ratio of longitudinal strain in the two will be (a) 1 : 16 (b) 16 : 1 (c) 1 : 64 (d) 64 : 1 35. A weight of 200 kg is suspended by vertical wire of length 600.5 cm. The area of cross-section of wire is 1mm2 . When the load is removed, the wire contracts by 0.5 cm. The Young's modulus of the material of wire will be (a) 2.35 × 10 12N/m2 (b) 1.35 × 10 10N/m2 (c) 13.5 × 10 11N/m2 (d) 23.5 × 10 9N/m2 36. If a load of 9 kg is suspended on a wire, the increase in length is 4.5 mm. The force constant of the wire is (a) 0.49 × 10 4N/m (b) 1.96 × 10 4N/m (c) 4.9 × 10 4N/m (d) 0.196 × 10 4N/m 37. The ratio of diameters of two wires of same material is n : 1. The length of wires are 4 m each. On applying the same load, the increase in length of thin wire will be (a) 2 n times (b) n times (c) 2n times (d) None of the above 38. Longitudinal stress of 1kg/mm2 is applied on a wire. The percentage increase in length is (Y = 10 11N/m2 ) (a) 0.002 (b) 0.001 (c) 0.003 (d) 0.01 39. A steel wire is stretched with a definite load. If the Young's modulus of the wire is Y. For decreasing the value of Y (a) Radius is to be decreased (b)Radius is to be increased (c) Length is to be increased (d) None of the above 40. The interatomic distance for a metal is 3 × 10 −10m. If the interatomic force constant is 3.6 × 10 −9N/Å, then the Young's modulus in N/m2 will be (a) 1.2 × 10 11 (b) 4.2 × 10 11 (c) 10.8 × 10 −19 (d) 2.4 × 10 10 41. Two identical wires of rubber and iron are stretched by the same weight, then the number of atoms in the iron wire will be (a) Equal to that of rubber (b)Less than that of the rubber (c) More than that of the rubber (d) None of the above 42. The force constant of a wire does not depend on (a) Nature of the material (b) Radius of the wire (c) Length of the wire (d) None of the above 43. The elasticity of invar (a) Increases with temperature rise (b)Decreases with temperature rise (c) Does not depend on temperature (d)None of the above