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Q77 (IAS/2007) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

Four wires of same material and of dimensions as under are stretched by a load of same magnitude separately. Which one of them will be elongated maximum?

Result
Your answer:  ·  Correct: C
Explanation

Elongation under a given tensile load is ΔL = (F·L)/(A·Y), so ΔL is proportional to L/A for the same material and load. For circular wires A ∝ d^2, hence ΔL ∝ L/d^2. Compute relative values (L/d^2) for each option (using mm for diameter): (1) 1/(2^2)=0.25, (2) 2/(2^2)=0.50, (3) 3/(1.5^2)=3/2.25≈1.33, (4) 1/(1^2)=1.00. The largest L/d^2 (≈1.33) corresponds to the 3 m wire of 1.5 mm diameter, so option 3 is elongated the most.

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