On this page
Stretching a steel wire by hanging a few kilograms on it changes its length by less than a millimetre. Searle's apparatus is built to measure that tiny change reliably, and the experiment is a good lesson in which measurement controls your final error. This post explains how the apparatus works, works a full set of sample readings two ways, and answers the question the lab manual leaves open: which reading matters most?
Where is this experiment in the syllabus?
The CBSE Physics curriculum for 2026-27 lists "To determine Young's modulus of elasticity of the material of a given wire" as the first experiment in Section B of the Class 11 practicals. The JEE (Main) 2026 syllabus includes Young's modulus of a metallic wire under Experimental Skills. The JEE (Advanced) 2026 Information Brochure lists "Young's modulus - elasticity of the material" among experiments for error analysis. Check the documents for your year.
How does Searle's apparatus work?
Experiment 9 of the NCERT Class 11 physics lab manual describes it. Two long wires of the same material hang from one rigid support. Each carries a metal frame, and the frames are hinged so they can slide past each other vertically. A spirit level rests on a crossbar between them, on a fixed knife edge at one end and the tip of a micrometer screw at the other.
The reference wire carries a constant weight to keep it taut.
The experimental wire carries a hanger, loaded in steps of 0.5 kg.
When the experimental wire stretches, its frame drops, the level tilts and the bubble moves. You turn the micrometer until the bubble is centred again. The screw's movement is the extension.
Why two wires? Anything that affects both equally, such as a change in room temperature or a slight sag of the support, moves both frames together and does not tilt the level. Only the extra stretch of the loaded wire is measured.
The principle is Hooke's law. For a wire of length L and radius r stretched by l under load M:
Y = MgL / (πr²l)
A worked set of readings
Sample numbers for a steel wire, g = 9.8 m/s².
Length L = 2.50 m.
Diameter from a screw gauge, measured at five places in two perpendicular directions as the manual asks: mean d = 0.60 mm, so r = 0.30 mm = 3.0 × 10⁻⁴ m.
Micrometer readings (mean of loading and unloading), in cm: 0.5 kg: 0.272, 1.0 kg: 0.294, 1.5 kg: 0.314, 2.0 kg: 0.337, 2.5 kg: 0.359, 3.0 kg: 0.380, 3.5 kg: 0.401, 4.0 kg: 0.424.
Half-table method. The manual pairs each reading with the one 1.5 kg heavier:
2.0 kg − 0.5 kg: 0.337 − 0.272 = 0.065 cm
2.5 kg − 1.0 kg: 0.359 − 0.294 = 0.065 cm
3.0 kg − 1.5 kg: 0.380 − 0.314 = 0.066 cm
Mean extension for 1.5 kg: l = 0.0653 cm = 6.53 × 10⁻⁴ m. (The manual's printed formula for this mean has a misprint in its subtractions, so work from these differences.)
Y = (1.5 × 9.8 × 2.50) / (π × (3.0 × 10⁻⁴)² × 6.53 × 10⁻⁴) = 36.75 / 1.846 × 10⁻¹⁰ = 1.99 × 10¹¹ N/m²
The NCERT chapter on mechanical properties of solids uses 2.0 × 10¹¹ N/m² for structural steel, so the result is sensible.
Graph method. Plot extension against load. Using all eight sample readings, the best line has slope 0.0433 cm/kg = 4.33 × 10⁻⁴ m/kg. Then Y = gL / (πr² × slope) = 2.00 × 10¹¹ N/m².
Which measurement controls the error?
The manual's discussion asks which quantity most affects the accuracy of Y. Add the fractional errors, taking each as the least count of the instrument used:
L: 0.1 cm in 250 cm = 0.04 percent.
l: micrometer least count 0.001 cm in 0.0653 cm = 1.5 percent.
r: r is squared, so its error counts twice. 0.01 mm in 0.60 mm is 1.7 percent, doubled to 3.3 percent.
Total: about 4.9 percent, so Y = (1.99 ± 0.10) × 10¹¹ N/m². The diameter accounts for two-thirds of the uncertainty. That is why the manual asks for ten diameter readings rather than one, and why a long wire helps: a larger L gives a larger l for the same load.
Common mistakes and how to avoid them
Using diameter as radius. That makes Y four times too small.
Mixing units. Put L, r and l all in metres before you divide.
Reading straight after loading. The manual asks you to wait before levelling the bubble each time, so the wire settles.
Backlash. Turn the micrometer in one direction only when you approach the setting.
Overloading. Stay well within the elastic limit, or the unloading readings will not match.
For the theory and more problems, see our post on elasticity and Young's modulus. For reading the screw gauge itself, see vernier and screw gauge readings, and for combining errors, error propagation in measurements.
A practice routine
Recompute Y from the sample readings, both ways, on paper.
Redo the error estimate with d = 0.40 mm and see how the percentage changes.
Explain aloud, in two sentences, what the reference wire is for.
In the lab, record loading and unloading readings side by side and compare them before you calculate.
If a step in the calculation does not make sense, the Fermi Problem Library has worked problems with a step-by-step solver that explains the reasoning rather than printing an answer.
Next step: measure one wire's diameter in ten places tonight and see how much the readings actually vary.
