Title 9.MECHANICAL PROPERTIES OF SOLIDS - Questions.pdf ✅

9.MECHANICAL PROPERTIES OF SOLIDS (1.)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.) 2 yx 2 (c.) 1 2 y 2x (d.) 1 2 yx 2 (2.)The elastic energy stored per unit volume in a stretched wire is (a.) 1 2 (Young modulus)(Strain) 2 (b.) 1 2 (Stress)(Strain) 2 (c.) 1 2 Stress Strain (d.) 1 2 (Young modulus)(Stress) (3.)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 modulii of the materials, then (a.) YB = 2YA (b.) YA = YB (c.) YB = 3YA (d.) YA = 3YB (4.)A cube is subjected to a uniform volume compression. It the side of the cube decreases by 2%, the bulk strain is (a.) 0.02 (b.) 0.03 (c.) 0.04 (d.) 0.06 (5.)The length of a rubber cord is l1 metre when the tension is 4 N and l2 metre when the tension is 6N. The length when the tension is 9 N, is (a.) (2.5l2 − 1.5l1 )m (b.) (6l2 − 1.5l1 )m (c.) (3l2 − 2l1 )m (d.) (3.5l1 − 2.5l1 )m (6.)A wire elongates by l mm when a load W is hanged from it. If the wire goes over a pulley and two weights W each are hung at the two ends, the elongation of the wire will be (in mm) (a.) l (b. ) 2l (c.) Zero (d.) l 2 (7.)Two similar wires under the same load yield elongation of 0.1 mm and 0.05 mm respectively. If the area of cross-section of the first wire is 4 mm2 , then the area of cross section of the second wire is (a.) 6 mm2 (b.) 8 mm2 (c.) 10 mm2 (d.) 12 mm2 (8.)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 (9.)Coefficient of isothermal elasticity Eθ and coefficient of adiabatic elasticity Eφ are related by (γ = Cp/Cv) (a.) Eθ = γEφ (b.) Eφ = γEθ (c.) Eθ = γ/Eφ (d.) Eθ = γ 2Eφ (10.)When a force is applied on a wire of uniform cross sectional area 3 × 10−6m2 and length 4m, the increase in length is 1 mm. Energy stored in it will be ( Y = 2 × 1011)Nm−2 ) (a.) 6250 J (b.) 0.177 J (c.) 0.075 J (d.) 0.150 J (11.)Longitudinal stress of 1 N/mm2 is applied on a wire. The percentage increase in length is (Y = 1011N/m2 ) (a.) 0.002 (b.) 0.001 (c.) 0.003 (d.) 0.01 (12.)Find the extension produced in a copper of length 2 m and diameter 3 mm, when a force of 30 N is applied. Young’s modulus for copper = 1.1 × 1011Nm−2 (a.) 0.2 mm (b.) 0.04 mm (c.) 0.08 mm (d.) 0.68 mm X 60o B A Y O 30o Stress Strain
(13.)A wire of length 2L and radius r is stretched between A and B without the application of any tension. If Y is the Young’s modulus of the wire and it is stretched like ACB, then the tension in the wire will be (a.) πr 2Yd 3 2L 2 (b.) πr 2Yd 2 2L 2 (c.) πr 2Y.2L 2 d2 (d.) πr 2Y.2L d (14.)A wire of length L and radius r fixed at one end and a force F applied to the other end produces an extensionl. The extension produced in another wire of the same material of length 2L and radius 2r by a force 2F, is (a.) l (b.) 2 l (c.) 4 l (d.) l 2 (15.)Write copper, steel, glass and rubber in order of increasing coefficient of elasticity. (a.) Steel, rubber, copper, glass (b.) Rubber, copper, steel, glass (c.) Rubber, glass, steel, copper (d.) Rubber, glass, copper, steel (16.)The relation between γ, η and K for a elastic material is (a.) 1 η = 1 3γ + 1 9K (b.) 1 K = 1 3γ + 1 9η (c.) 1 γ = 1 3K + 1 9η (d.) 1 γ = 1 3η + 1 9K (17.)A ball falling in a lake of depth 200 m shows a decrease of 0.1% in its volume at the bottom. The bulk modulus of elasticity of the material of the ball is (Take g=10 ms −2 ) (a.) 109 Nm−2 (b.) 2 × 109 Nm−2 (c.) 3 × 109 Nm−2 (d.) 4 × 109 Nm−2 (18.)A steel wire of 1m long and 1mm2 cross section area is hang from rigid end. When weight of 1kg is hung from it then change in length will be (given Y = 2 × 1011N/m2 ) (a.) 0.5 mm (b.) 0.25 mm (c.) 0.05 mm (d.) 5 mm (19.)Bulk modulus of water is 2 × 109 Nm−2 . The change in pressure required to increase the density of water by 0.1% is (a.) 2 × 109 Nm−2 (b.) 2 × 108 Nm−2 (c.) 2 × 106 Nm−2 (d.) 2 × 104 Nm−2 (20.)A graph is shown between stress and strain for a metal. The part in which Hooke’s law holds good is (a.) OA (b.) AB (c.) BC (d.) CD (21.)The dimensions of four wires of the same material are given below. In which wire the increase in length will be maximum ? (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 (22.)Which of the following relations is true (a.) 3Y = K(1 − σ) (b.) K = 9ηY Y+η (c.) σ = (6K + η)Y (d.) σ = 0.5Y−η η (23.)The upper end of a wire of radius 4 mm and length 100 cm is clamped and its other end is twisted through and angle of 30°. Then angle of shear is (a.) 0.012° (b.) 0.12° (c.) 1.2° (d.) 12° (24.)Two exactly similar wires of steel and copper are stretched by equal forces. If the difference in their elongations is 0.5cm, the elongation (l) of each wire is Ys (steel) = 2.0 × 1011N/m2 Yc (copper) = 1.2 × 1011N/m2 (a.) ls = 0.75cm, lc = 1.25cm (b.) ls = 1.25cm, lc = 0.75cm (c.) ls = 0.25cm, lc = 0.75cm (d.) ls = 0.75cm, lc = 0.25cm Stress A B C D O Strain
(25.)The graph is drawn between the applied force F and the strain (x) for a thin uniform wire. The wire behaves as a liquid in the part (a.) ab (b.) bc (c.) cd (d.) oa (26.)A cube is compressed at 0°C equally from all sides by an external pressure p. By what amount should be temperature be raise to bring to back to the size it had before the external pressure was applied ? (Given K is bulk modulus of elasticity of the material of the cube and α is the coefficient of linear expansion.) (a.) p Kα (b.) p 3Kα (c.) 3πα p (d.) K 3p (27.)A wire of length 50 cm and cross sectional area of 1 sq. mm is extended by 1 mm. The required work will be (Y = 2 × 1010Nm−2 ) (a.) 6 × 10−2 J (b.) 4 × 10−2 J (c.) 2 × 10−2 J (d.) 1 × 10−2 J (28.)A cube is shifted to a depth of 100 m in a lake. The change in volume is 0.1%. The bulk modulus of the material is nearly (a.) 10 Pa (b.) 104 Pa (c.) 107 Pa (d.) 106 Pa (29.)The length of an elastic spring is a metres when a force of 4 N is applied, and b metres when the 5 N force is applied. Then the length of the spring when the 9 N force is applied is (a.) a + b (b.) 9b – 9a (c.) 5b − 4a (d. ) 4a – 5b (30.)Identify the incorrect statement. (a.) Young’s modulus and shear modulus are relevant only for solids (b.) Bulk modulus is relevant for solids, liquids and gases (c.) Alloys have larger values of Young’s modulus than metals (d.) Metals have larger values of Young’s modulus than elastomers (31.)If the work done in stretching a wire by 1 mm is 2 J, the work necessary for stretching another wire of same material but with double radius of cross-section and half the length by 1 mm is (a.) 1 4 J (b.) 4 J (c.) 8 J (d.) 16 J (32.)In the Young’s experiment, If length of wire and radius both are doubled then the value of Y will become (a.) 2 times (b.) 4 times (c.) Remains same (d.) Half (33.)Two wires A and B of same length, same area of cross-section having the same Young’s modulus are heated to the same range of temperature. If the coefficient of linear expansion of A is 3/2 times of that of wire B. The ratio of the forces produced in two wires will be (a.) 2/3 (b.) 9/4 (c.) 4/9 (d.) 3/2 (34.)Two rods A and B of the same material and length have their radii r1 and r2 respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio of the angle of twist at the end of A and the angle of twist at the end of B is (a.) r2 4 r1 4 (b.) r1 4 r2 4 (c.) r2 2 r1 2 (d.) r1 2 r2 2 (35.)Which of the following substance has the highest elasticity? (a.) Steel (b.) Copper (c.) Rubber (d.) Sponge (36.)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 F O a b c d X x
(d.) F/4 (37.)A force of 103 newton stretches the length of a hanging wire by 1 millimetre. The force required to stretch a wire of same material and length but having four times the diameter by 1 millimetre is (a.) 4 × 103N (b.) 16 × 103N (c.) 1 4 × 103N (d.) 1 16 × 103N (38.)A rod of length l and radius r is joined to a rod of length l 2 and radius r/2 of same material. The free end of small rod is fixed to a rigid base and the free end of larger rod is given a twist of θ 0 , the twist angle at the joint will be (a.) θ 4 (b.) θ 2 (c.) 5θ 6 (d.) 8θ 9 (39.)If Eθ and Eφ denote the isothermal and adiabatic elasticities respectively of a gas, then Eθ Eφ (a.) < 1 (b.) > 1 (c.) = 1 (d.) = 3.2 (40.)The bulk modulus of an ideal gas at constant temperature (a.) Is equal to its volume V (b.) Is equal to p/2 (c.) Is equal to its pressure p (d.) Can not be determined (41.)The Young’s modulus of brass and steel are 10 × 1010 Nm−2 and 2 × 1011 Nm−2 respectively. A brass wire and a steel wire of the same length are extended by 1 mm under the same force. The radii of the brass and steel wires are RB and RS respectively. Then (a.) RA = √2 RB (b.) RS = RB √2 (c.) RS = 4 RB (d.) RS = RB 4 (42.)The length of a wire is increased by 1 mm on the application of a given load. In a wire of the same material, but of length and radius twice that of the first, on the application of the same load, extension is (a.) 0.25 cm (b.) 0.5 cm (c.) 2 mm (d.) 4 mm (43.)A brass rod of cross-sectional area 1cm2 and length 0.2m is compressed lengthwise by a weight of 5 kg. If Young’s modulus of elasticity of brass is 1 × 1011N/m2 and g = 10m/ sec2 , then increase in the energy of the rod will be (a.) 10−5 J (b.) 2.5 × 10−5 J (c.) 5 × 10−5 J (d.) 2.5 × 10−4 J (44.)An aluminium rod, Young’s modulus 7.0 × 109N m−2 , has a breaking strain of 0.2%. The minimum cross-sectional area of the rod in m2 in order to support a load of 104 N is (a.) 1 × 10−2 (b.) 1.4 × 10−3 (c.) 1.0 × 10−3 (d.) 7.1 × 10−4 (45.)A wire extends by 1 mm when a force is applied. Double the force is applied to another wire of same material and length but half the radius of cross-section. The elongation of the wire in mm will be (a.) 8 (b.) 4 (c.) 2 (d.) 1 (46.)Equal torsional torques act on two rods x and y having equal length. The diameter of rod y is twice the diameter of rod x. If θx and θy are the angles of twist, then θx θy = (a.) 1 (b.) 2 (c.) 4 (d.) 16 (47.)To keep constant time, watches are fitted with balance wheel made of (a.) Invar (b.) Stainless steel (c.) Tungsten (d.) Platinum (48.)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