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1. A steel wire of length 4.7 m and cross - section 3.0 X 10-5 m2 stretches by the same amount as a copper wire of length 3.5 m and cross - section 4.0 X 10-5 m2 under a given load. What is the ratio of the Young's modulus of steel to that of copper ?
2. The stress - strain for a given material What are (a) Young's modulus and (b) approximate yield strength for this material ?
3.The stress - strain graphs for materials A and B are.
The graphs are drawn to the same scale.
(a) Which of the material has greater Young's modulus ?
(b) Which material is more ductile ?
(c) Which is more brittle ?
Which of the two is stronger material ?
As the slope of stress - strain graph for material A is higher than that for material B, so material A has greater Young's modulus than B.
(b) Material A is more ductile than B, because it has larger range of plastic extension between its elastic limit and fracture point.
(c) Material B is more brittle than A, because its plastic range of extension is very small.
(d) Material A is stronger than B, because it can withstand stress before breaking.
4. Read each of the statements below carefully and state, with reasons, if it is true or false.
(a) The modulus of elasticity of rubber is greater then that of steel.
(b) The stretching of a coil is determined by its shear modulus.
(a) False. When steel and rubber are subjected to the same deforming force, less extension and hence less strain is produced in the steel than the rubber and as
so Υ is more in case of steel then in the case of rubber.
(b) True. When the coil is stretched, there is no change in the length or the volume of the wire used in the coil. There is only a change in the shape of the spring, so shear modulus in involved.
5. Two wires of diameter 0.25 cm, one made of steel and other made of brass are loaded . The unloaded length of steel wire is 1.5 m and that of brass wire is 1.0 m. Young's modulus of steel is 2.0 X 1011 Pa and that of brass is 0.91 X 1011 Pa. Compute the elongations of steel and brass wires. (1 Pa = 1 Nm-2).
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6. The edge of an aluminium cube is 10 cm long. One face of the cube is firmly fixed to a vertical wall. A mass of 100 kg is then attached to the opposite face of the cube. The shear modulus of aluminium is 25 G Pa. What is the deflection of this face ? ( 1 Pa = 1 Nm-2).
7. Four identical hollow cylindrical columns of mild steel support a big structure of mass 50,000 kg. The inner and outer radii each column are 30 cm and 40 cm respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column. The Young's modulus of steel is 2.0 X 1011 Pa.
8. A piece of copper having a rectangular cross - section of 15.2 mm X 19.1 mm is pulled in tension with 44,500 N force, producing only elastic deformation. Calculate the resulting strain.
9. A steel cable with a radius of 1.5 cm supports a chairlift at a ski area. If the maximum stress is not to exceed 108 Nm-2, what is the maximum load the cable can support ?
10. A rigid bar of mass 15 kg is supported symmetrically by three wires each 2.0 m long. Those at each end are of copper and the middle one is of iron. Determine the ratios of their diameters if each is to have the same tension.
11. A 14.5 kg mass, fastened to the end of a steel wire of unstretched length 1.0 m, is whirled in a vertical circle with an angular velocity of 2 rev/s at the bottom of the circle. The cross - sectional area of the wire is 0.005 cm2. Calculate the elongation of the wire when the mass is at the lowest point of its path.
12. Compute the bulk modulus of water from the following data : Initial volume = 100.0 litre, pressure increase = 100.0 atm, final volume = 100.5 litre ( 1 atm = 1.013 X 105 Pa).
13.What is the density of ocean water at a depth,where the pressure is 80.0 atm, given that its density at the surface is 1.03 X 103 kgm-3 ? Compressibility of water = 45.8 X 10-11 Pa-1. Given 1 atm = 1.013 X 105 Pa.
14. Compute the fractional change in volume of a glass slab, when subjected to a hydraulic pressure of 10 atm.
15. Determine the volume contraction of a solid copper cube, 10 cm on an edge, when subjected to a hydraulic pressure of 7.0 X 106 Pa.
16. How much should the pressure on a litre of water be changed to compress it be 0.10 % ?
17. Anvils made of single crystals of diamond, with the shape as shown are used to investigate behaviour of materials under very high pressures. Flat faces at the narrow end of the anvil have a diameter of 0.45 mm, and the wide ends are subjected to a compressional force of 50,000 N. What is the pressure at the tip of the anvil ?
18.A rod length 1.05 m having negligible mass is supported at its ends by two wires of steel (wire A) and aluminium (wire B) of equal lengths as shown. The cross - sectional areas of wires A and B are 1.0 mm2 and 2.0 mm2 respectively. At what point along the rod should a mass m be suspended in order to produce (a) equal stress and (b) equal stains in both steel aluminum wires ?
19. A mild steel wire of length 1.0 m and cross - sectional area 0.50 X 10-2 cm2 is stretched well within its elastic its elastic limit, horizontally between two pillars. A mass of 100 g is suspended from the lid - point os wire. Calculate the depression at the mid - point.
20. Two strips of metal are riveted together at their ends by four rivets, each of diameter 6.0 mm. What is the maximum tension that can be exerted by the riveted strip if the shearing stress on the rivet is not to exceed 2.3 X 109 Pa ? Assume that each rivet is to carry one quarter of the load.
21. The Marina trench is located in the Pacific Ocean and at one place it is nearly eleven km beneath the surface of water. The water pressure at the bottom of the trench is about 1.1 X 108 Pa. A steel ball of initial volume 0.32 m3 is dropped into the ocean and falls to the bottom of the trench. What is the change in the volume of the ball when it reaches to the bottom ?
