More practice questions

4. Q4. A steel rod must hang a load of 10 000 kg without yielding. Steel’s yield strength is 250 × 10^⁶ N m^⁻². Find the least cross-section and the corresponding radius. Take g = 9.8 m s^⁻².

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   A = mg/σ_y = 10 000 × 9.8/(250 × 10^⁶), about 3.92 × 10^⁻⁴ m^². The radius is √(A/π), about 1.1 × 10^⁻² m, that is, about 1.1 cm. (A real design would use a larger rod, for safety.)

5. Q5. NCERT Table 8.1 gives bone an ultimate strength of 170 × 10^⁶ N m^⁻² under compression. What compressive load would crush a thighbone of effective radius 2.0 cm? Take g = 9.8 m s^⁻².

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   A = π(2.0 × 10^⁻²)^², about 1.26 × 10^⁻³ m^². The load is 170 × 10^⁶ × 1.26 × 10^⁻³, about 2.1 × 10^⁵ N, the weight of about 22 000 kg. Bones are very strong in compression.

6. Q6. Using NCERT Table 8.1 (copper: Young’s modulus 110 × 10^⁹ N m^⁻², yield strength 200 × 10^⁶ N m^⁻²), estimate the largest strain copper can take and still recover.

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   Roughly σ_y divided by the slope of the straight part: 200 × 10^⁶/(110 × 10^⁹), about 1.8 × 10^⁻³, less than 0.2%.