In Searle’s experiment a wire is exactly 2 m long. Its extension is (0.8 ± 0.05) mm for an exactly 1 kg load, and its diameter is (0.4 ± 0.01) mm. Take g = 9.8 m s⁻² exactly. If Young’s modulus is (n ± 0.2)×10¹¹ N m⁻², find n.
Physics · Mixed Chapter
JEE Mains

Question

In Searle’s experiment a wire is exactly 2 m long. Its extension is (0.8 ± 0.05) mm for an exactly 1 kg load, and its diameter is (0.4 ± 0.01) mm. Take g = 9.8 m s⁻² exactly. If Young’s modulus is (n ± 0.2)×10¹¹ N m⁻², find n.

Physics · Mixed Chapter

G1 Physics · Accepted Answer

Step 1 — Young’s modulus expression: Y = (FL)/(AΔL) = (4mgL)/(πd²ΔL). Step 2 — Put measured values in SI: m = 1 kg; L = 2 m; d = 4×10⁻⁴ m; ΔL = 8×10⁻⁴ m. Step 3 — Central value: Y = [4×1×9.8×2]/[π(4×10⁻⁴)²(8×10⁻⁴)] ≈ 1.95×10¹¹ N m⁻². Step 4 — Uncertainty estimate: δY/Y ≈ 2(0.01/0.4)+(0.05/0.8) ≈ 0.1125, giving δY ≈ 0.22×10¹¹ N m⁻². Step 5 — Round as given: Y ≈ (2.0 ± 0.2)×10¹¹ N m⁻², hence n = 2. Answer: 2.