Young S Modulus Searle S Method — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Young's Modulus (Searle's Method) Applicable for materials within their elastic limit (Hooke's Law region) and for wires of uniform cross-section. Define Young's Modulus Y = Stress / Strain. Calculate Longitudinal Stress = Force / Area = (Mg) / (pi r 2). Calculate Longitudinal Strain = Extension / Original Length = l / L. Substitute Stress and Strain into the definition: Y = (Mg / (pi r 2)) / (l / L). Rearrange to get Y = (MgL) / (pi r 2 l). The wire must obey Hooke's Law. The extension l must be small compared to L. Temperature must remain constant during the experiment. The wire should be free of kinks. Confusing radius (r) with diameter (D) measured by screw gauge (r = D/2). Neglecting the fact that the error in radius contributes twice as much to the percentage error (due to r 2) compared to length or mass. Assuming the formula works beyond the yield point.