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A vertical steel rod of cross-sectional area 16 cm² acts in parallel with two brass rods, each of cross-sectional area 10 cm², and together they support a load of 5000 kg. The rods are arranged so that all three undergo the same strain. Taking Y for steel = 2.0*10⁶ N/cm² and Y for brass = 1.0*10⁶ N/cm² and g = 9.8 m/s², what is the stress developed in the steel rod?
- 1884.6 N/cm²
- 942.3 N/cm²
- 3062.5 N/cm²
- 1531.3 N/cm²
Correct answer: 1884.6 N/cm²
Solution
Because the rods share the load and deform equally (same strain), the stress in each is proportional to its Young's modulus, so steel carries twice the stress of brass. Combining this with the load-balance equation over the total cross-sectional areas (16 cm² of steel and 2*10 = 20 cm² of brass) and the total weight 5000*9.8 = 49000 N gives a steel stress of about 1884.6 N/cm².
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