Physics-11 : 8: Mechanical Properties of Solids - Flashcards

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What is stress?
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The restoring force per unit area. Magnitude of stress = \( F/A \).
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# Question Answer
1 What is stress? The restoring force per unit area. Magnitude of stress = \( F/A \).
2 What is Hooke's law? For small deformations, stress is proportional to strain: stress = \( k \) × strain, where \( k \) is the modulus of elasticity.
3 Which material among steel, copper, aluminium and brass is the most elastic? Steel.
4 What is the SI unit of shear modulus? N m⁻² or Pa.
5 Which state of matter is the least compressible? Solids.
6 The average depth of the Indian Ocean is 3000 m. What is the fractional compression of water at the bottom? (\( B = 2.2 \times 10^9 \) N m⁻²) 1.36%.
7 What is the form of Hooke's law for tensile or compressive stress? \( \frac{F}{A} = Y \frac{\Delta L}{L} \).
8 Is bulk modulus relevant for solids, liquids and gases? Yes.
9 Is the Young's modulus of rubber greater than that of steel? No. The Young's modulus of rubber is much smaller than that of steel.
10 Why is the bulk modulus of water much larger than that of air? Because the molecules in water are more closely packed and more strongly bound than in air.
11 A copper wire (L=2.2 m) and a steel wire (L=1.6 m), both of diameter 3.0 mm, are joined end to end and stretched; the net elongation is 0.70 mm. What load was applied? (\(Y_c=1.1\times10^{11}\), \(Y_s=2.0\times10^{11}\) N m⁻²) ≈ \(1.8 \times 10^2\) N (176.7 N), found from \(\Delta L_c/\Delta L_s=(Y_s/Y_c)(L_c/L_s)=2.5\), giving \(\Delta L_c=5.0\times10^{-4}\) m and \(\Delta L_s=2.0\times10^{-4}\) m.
12 Does a deforming force applied along one direction produce strain only along that direction? No. It generally produces strains in other directions too (e.g., a wire's lateral dimension changes under longitudinal strain); this cross-strain is described by a separate elastic constant, the Poisson ratio.
13 Does tensile or compressive stress change a body's shape, volume, or both? It changes shape (length) but not volume.
14 To reduce the bending (sag) of a loaded beam, is increasing the depth d or the breadth b more effective? Increasing the depth d, since \(\delta \propto d^{-3}\) but only \(\delta \propto b^{-1}\).
15 Assertion: The stretching of a coil spring is governed by the shear modulus of its material. Reason: A copper coil spring has more tensile strength than a steel spring of the same dimensions. Are these true? Assertion is true (stretching a coil twists the wire, which is a shear deformation); Reason is false — from Table 8.1, steel's yield strength (250×10⁶ N m⁻²) is greater than copper's (200×10⁶ N m⁻²), so steel has more tensile strength, not copper. (NEET 2022)
16 A spherical object of bulk modulus B is subjected to a uniform pressure p. What is the fractional decrease in its radius? \( \Delta R/R = p/(3B) \), since \(\Delta V/V=-p/B\) and \(V\propto R^3\) gives \(\Delta R/R=\tfrac{1}{3}(\Delta V/V)\). (NEET 2017)