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Physics

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Properties of Matter Session

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Session Objectives

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Session Objective Elasticity – Concept Stress and Strain Hooke's law and Young's modulus Elastic potential energy in a strained body Poisson's ratio Shear modulus Bulk modulus

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A F F Force per unit area is stress. Fractional change in shape brought by application of stress is called strain. Stress and Strain

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Hooke’s Law Hooke’s law is valid for metals, within limit of proportionality and states that for a body, applied stress is proportional to strain

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Questions

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According to Hooke’s law of elasticity,if stress is increased,the ratio of stress to strain (a)Increase (b) decrease (c) Becomes zero(d) Remains Constant Illustrative Problem Solution : Hooke’s laws states that “stress upon strain is constant for a particular material”

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Elasticity Proportionality Limit Elastic Limit Fracture point A B C stressstress s t r a i n

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Young’s Modulus A L L+L FF

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Shear Modulus xx h A F -F

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V Bulk Modulus F F V-V

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Poisson Ratio The ratio of the lateral strain to longitudinal strain is constant for a given material. This is called Poisson’s ratio. It is represented by. It has no units and dimension.

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Strain Energy Strained Energy Strain energy per unit volume

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Questions

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If in a wire of Young’s modulus Y, longitudinal strain X is produced,then the value of potential energy stored in per unit volume will be (a)YX 2 (b) 2 YX 2 (c) 0.5Y 2 X(d)0.5 YX 2 Illustrative Problem

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Potential energy stored = ½ x strain x stress Stress = Strain x Modulus = XY PE = 0.5 YX 2 Solution

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Class Test

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Class Exercise - 1 The bulk modulus of a perfectly rigid body is equal to (a) zero (b) infinite (c) unity (d) a non-zero constant

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Solution Hence answer is (b). for perfectly rigid body is zero. Hence, is infinite.

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Class Exercise - 2 If a body is strained, its internal energy (a)decreases (b) Increases (c) remains unchanged (d) changes randomly

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Solution Upon straining, body gets elastic potential energy. Thus, total internal energy increases. Hence answer is (b).

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Class Exercise - 3 A material has Poisson ratio 0.50 of a uniform rod if it suffers a longitudinal strain of 2 × 10 -3, Then percentage change in volume is (a) 0.6(b) 0.4 (c) 0.2(d) zero

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Solution Let the initial and final volumes are v and v + dv. Hence answer is (d).

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Class Exercise - 4 The length of a metal wire is when the tension in it is T 1 and is when tension is T 2. The unstrectched length of the wire is

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Solution Hence answer is (c). Let the original length

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Class Exercise - 5 A spherical ball contracts in volume by 0.0098% when it is subjected to a pressure of 100 atm. Calculate its bulk modulus. (a) 1.02 × 10 6 atm(b) 1.02 × 10 4 atm (c) 1.02 × 105 atm(d) 1.02 × 10 3 atm

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Solution = 100 atm = 1.02 × 10 6 atm Hence answer is (a).

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Class Exercise - 6 A metal cube of side 0.1 m has its upper face displaced by 0.2 mm when a shearing stress of 10 6 kg weight is applied it. The shear modulus of the cube is (a) 4.9 × 10 11 N/m 2 (b) 9.8 × 10 11 N/m 2 (c) 4.9 × 10 9 N/m 2 (d) 9.8 × 10 9 N/m 2

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Solution Hence answer is (a). = 4.9 × 10 11 N/m 2

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Class Exercise - 7 A rope of 1 cm in diameter breaks if the tension in it exceeds 50 N. The maximum tension that may be given to a similar rope of diameter 2 cm is (a) 500 N(b) 250 N (c) 1,000 N(d) 2,000 N

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Solution Hence answer is (d). = 500 × 4 = 2000 N

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Class Exercise - 8 What is the volume change of a solid copper cube, 40 mm on each edge, when subjected to a pressure of 2 × 10 7 pa. Bulk modulus of copper is 1.25 × 10 11 N/m 2 (a) 10.24 × 10 2 mm 3 (b) 1.024 × 10 2 mm 3 (c) 10.24 mm 3 (d) 102. 4 × 10 2 mm 3

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Solution Hence answer is (c). = 10.24 mm 3

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Class Exercise - 9 An aluminum rod, Young’s modulus 7 × 10 9 N/m 2 has a breaking strain of 0.2%. The minimum cross-sectional area of rod in m 2 to support a load of 10 4 N is (a) 1 × 10 –2 (b) 1 × 10 –3 (c) 1.4 × 10 –2 (d) 7.1 × 10 –4

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Solution Y = 7 × 10 9 N/m 2 F = 10 4 N Hence answer is (d).

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Class Exercise - 10 Two wires of same material and length but diameters in the ratio 1 : 2 are stretched by the same force. The potential energy per unit volume of two wires will be in the ratio (a) 16 : 1(b) 4 : 1 (c) 1 : 4(d) 1 : 1

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Solution Hence answer is (a).

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Thank you

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