In Searle's experiment, wire diameter =0.050 cm (screw-gauge LC 0.001 cm), length=110.0 cm (scale LC 0.1 cm), load=50 N, extension=0.125 cm (micrometer LC 0.001 cm). Maximum error in Young's modulus is P×10⁹ N m⁻². Find P.

Question

G1 Physics · Accepted Answer

Y=4FL/(πd²ΔL)≈2.24×10¹¹ N m⁻². Maximum fractional error=2(0.001/0.050)+(0.1/110)+(0.001/0.125)≈0.0489. Absolute error≈0.0489×2.24×10¹¹≈1.10×10¹⁰=11×10⁹ N m⁻². Hence P=11.