More practice questions

4. Q4. A steel cube of edge 5.0 cm has its base fixed. A force of 2.0 × 10^⁴ N acts along its top face. Find the angle of shear and the sideways shift of the top face. Take G = 84 × 10^⁹ N m^⁻² (NCERT Table 8.2).

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   Stress = 2.0 × 10^⁴/(0.05)^² = 8.0 × 10^⁶ N m^⁻². θ = stress/G = 8.0 × 10^⁶/(8.4 × 10^¹⁰), about 9.5 × 10^⁻⁵ rad. The shift is θL ≈ 9.5 × 10^⁻⁵ × 0.05 m, about 4.8 × 10^⁻⁶ m (4.8 µm).

5. Q5. How much elastic energy is stored per cubic metre of steel under a tensile stress of 1.0 × 10^⁸ N m^⁻²? Take Y = 2.0 × 10^¹¹ N m^⁻².

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   u = σ^²/(2Y) = (1.0 × 10^⁸)^²/(4.0 × 10^¹¹) = 2.5 × 10^⁴ J m^⁻³.

6. Q6. Using NCERT Table 8.3, find the compressibilities of water (B = 2.2 × 10^⁹ Pa) and of air at STP (B = 1.0 × 10^⁵ Pa). How many times more compressible is air?

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   Water: 1/(2.2 × 10^⁹), about 4.5 × 10^⁻¹⁰ Pa^⁻¹. Air: 1/(1.0 × 10^⁵) = 1.0 × 10^⁻⁵ Pa^⁻¹. Air is about 2.2 × 10^⁴ times as compressible as water.

7. Q7. A wire 3.0 m long, of cross-section 1.0 mm^², stretches by 2.73 mm under a load of 100 N. Find its Young’s modulus and suggest the metal, using NCERT Table 8.1.

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   Y = FL/(AΔL) = 100 × 3.0/(1.0 × 10^⁻⁶ × 2.73 × 10^⁻³), about 1.1 × 10^¹¹ N m^⁻², which matches copper.