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CBSE Test Paper 03, Chapter 9 Mechanical Properties of Solids, , 1. In constructing a large mobile, an artist hangs an aluminum sphere of mass 6.0 kg, from a vertical steel wire 0.50 m long and 2.5, , in cross-sectional area. On, , the bottom of the sphere he attaches a similar steel wire, from which he hangs a brass, cube of mass 10.0 kg. Compute the elongation. 1, a. 1.5 mm upper, 1.1 mm lower, b. 1.4 mm upper, 1.0 mm lower, c. 1.6 mm upper, 1.0 mm lower, d. 1.7 mm upper, 1.0 mm lower, 2. A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile, force of 400 N is applied to each end of the wire. What minimum diameter is required, for the wire? 1, a. 1.9 mm, b. 1.43 mm, c. 12.4 mm, d. 2.48 mm, 3. Determine the volume contraction of a solid copper cube, 10 cm on an edge, when, subjected to a hydraulic pressure of 7.0, , Pa. Bulk modulus of copper 140 GPa. 1, , a. 0.05, b. 0.12, c. 0.26, d. 0.08, 4. A specimen of oil having an initial volume of 600, increase of 3.6, , is subjected to a pressure, , Pa and the volume is found to decrease by 0.45, , what is the, , bulk modulus of the material? 1, a. 4.4, , Pa, , b. 5.0, , Pa, , c. 4.8, , Pa, 1/8
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d. 4.6, , Pa, , 5. Elastomers are materials 1, a. which cannot be stretched to cause large strains, b. which can be stretched to cause large strains, c. which can be stretched without corresponding stress, d. which cannot be stretched to beyond elastic limit, 6. When is a body said to be under compressional strain? 1, 7. The stretching of a coil spring is determined by its shear modulus. Why? 1, 8. An elastic wire is cut to half its original length. How would it affect the maximum load, that the wire can support? 1, 9. A particle is thrown upwards. It attains a height (h) after 5 seconds and again after 9s, when it comes back. What is the speed of the particle at a height h? 2, 10. 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 N m-2, what is the maximum load the cable can support? 2, 11. Write the characteristics of displacement. 2, 12. The edge of an aluminum 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 GPa. What is the vertical deflection of this face? 3, 13. The Young’s modulus of steel is 2.0, metal is 2.8, , 1011 N/m2. If the interatomic spacing for the, , 10-10 m, find the increase in the interatomic spacing for a force of 109 N, , m-2 and the force constant? 3, 14. The stress-strain graph for a metal wire is given in the figure. Up to the point B, the, wire returns to its original state O along the curve BAO, when it is gradually unloaded., Point E corresponds to the fracture point of the wire. 3, i. Up to which point of the curve, is Hook's law obeyed? This point is also called, 'Proportionality limit'., 2/8
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ii. Which point on the curve corresponds to elastic limit and yield point of the wire?, iii. Indicate the elastic and plastic regions of the stress-strain curve., iv. What change happens when the wire is loaded up to a stress corresponding to, point C on a curve, and then unloaded gradually?, , 15. Draw a typical stress-strain curve for a ductile metal and briefly explain the, important points (salient features) of the curve. 5, , 3/8
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CBSE Test Paper 03, Chapter 9 Mechanical Properties of Solids, , Answer, 1., , c. 1.6 mm upper, 1.0 mm lower, Explanation: given mass of aluminium sphere msph = 6.0 kg, length of steel wire Lsteel = 0.50 m, area of steel wire Asteel = 2.5, , 10-3 cm2, , mass of cube mcube =10 kg, net restoring force in lower wire i.e. tension T2 will be equal to weight of cube, i.e. T2 = mcube g = 10g, net restoring force in upper wire i.e. tension T1, T1 = msph g + T2 = 6g + 10g = 16g, standard valu for young modulus of steel y = 2, , 1011 N/m2, , for lower wire, , now for upper wire, , 2., , b. 1.43 mm, Explanation: Let Young's modulus of steel wire Y, , 4/8
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3., , a. 0.05 cm3, Explanation: Length of an edge of the solid copper cube, l = 10 cm = 0.1 m, Hydraulic pressure, p = 7.0 × 106 Pa, Bulk modulus of copper, B = 140 × 109 Pa, bulk modulus B =, , 4., , c. 4.8, , Pa, , Explanation: bulk modulus is defined as B=, here P is volume stress which is equal to presssure, , 5., , b. which can be stretched to cause large strains, Explanation: Substances like tissue of aorta (Present in the heart), rubber etc., which can be stretched to cause large strains are called elastomers. They show, large plastic range in stress-strain curve., , 6. When the deforming force is such that there is the decrease in the length of the body,, then the strain produced in the body is known as compressional strain., A body said to be under compressional strain, if a solid spheric body is placed inside a, fluid under high pressure, the body is said to be under hydraulic compression. In such, a case there is decrease in volume of the body without any change of its geometrical, shape., 7. The reason is that when a coil spring is stretched, there is neither a change in the, length of the coil (i.e., length of the wire forming the coil spring) nor a change in its, volume. Since the change takes place in the shape of the coil spring, its stretching is, determined by its shear modulus, , 5/8
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8. Since Breaking Stress, , ;, , breaking load = breaking stress, , area, , So, if cable is cut to half of its original length, there is no change in its area. Hence, there is no effect on the maximum load that the wire can support., 9. Let total height from ground is H, at t = 5s object is at a height h, Let velocity at h is u., velocity at top is zero., using equation v = u + at during upward motion, for downward motion from top to height h, , 10. Radius of the steel cable, r = 1.5 cm = 0.015 m, Maximum allowable stress, Maximum stress, Maximum force = maximum stress, , area of cross section, , Hence, the cable can support the maximum load of, 11., , i. It is a vector quantity having both magnitude and direction., ii. Displacement of a given body can be positive, negative or zero., , 12. Edge of the aluminium cube, L = 10 cm = 0.1 m, Area of face of cube, The mass attached to the cube, m = 100 kg, Shear modulus of aluminium,, applied force, Shear modulus,, vertical deflection of cube, , 6/8
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13. Given : young's modulus Y, interatomic spacing in metal,, applied force per unit area,, Let increase in interatomic spacing, Using relation, , for force constant F = - Kx, here, Area of cross section, , 14., , i. Hooke's law is obeyed up to point A of the stress-strain curve., ii. Point B on the curve corresponds to elastic limit and yield point of a given wire., iii. The region OB on the stress-strain curve represents the elastic region. The region, BD on the stress-strain curve represents the plastic region., iv. When the given wire is loaded up to a stress corresponding to point C on the curve, and then unloaded gradually, it does not regain its original configuration even on, complete unloading. The material has some strain left (OO'), which is called a, permanent set., , 15. The stress-strain curve is used to determine the relation between stress and strain for, a given material graphically. These graphs are different for different materials. The, typical stress-strain curve for a metal is shown in Figure., , 7/8
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The important features of the curve are as follows :, i. The curve is linear in the region from O to A. Here Hooke's law is obeyed and the, solid behaves like a perfectly elastic body., ii. In the region AB, stress is not proportional to strain, hence Hooke's law is not, obeyed. But the body behaves as an elastic body and on the removal of the load,, the body returns to its original dimension., iii. The point B is known as the yield point or elastic limit beyond which the body does, not remain elastic. The stress corresponding to the yield point is known as the, yield strength, , y, , of the material., , iv. Beyond yield point in the entire region BD, the strain increases rapidly even for a, small change in stress. Here the material is exhibiting plastic behaviour and the, region BD is called the region of plasticity., v. At any stage between B and D (say at point C), if the load is removed, the body does, not regain its original dimension and some strain is left behind, which is known as, "permanent set". Here even when stress is zero, strain is not zero., vi. The point D on the graph is the "ultimate tensile strength" ( u) of the material., vii. Beyond point D, additional strain is produced even by a reduced applied force and, at a point E fracture occurs. The given wire breaks into two pieces., viii. The region DE represents the region of ductility., , 8/8
