In a Searle's experiment, the diameter of the wire as measured by a screw gauge of least count $$0.001$$ cm is $$0.050cm$$. The length, measured by a scale of least count $$0.1$$ cm, is $$110.0cm$$. When a weight of $$50$$ N (measured$$ with no $$error) is suspended from the wire, the extension is measured to be $$0.125$$ cm by a micrometer of least count $$0.001$$ cm. Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.

Question

In a Searle's experiment, the diameter of the wire as measured by a screw gauge of least count $$0.001$$ cm is $$0.050cm$$.  The length, measured by a scale of least count $$0.1$$ cm, is $$110.0cm$$.  When a weight of $$50$$ N (measured$$ with no $$error) is suspended from the wire, the extension is measured to be $$0.125$$ cm by a micrometer of least count $$0.001$$ cm.  Find the maximum error in the measurement of Young's modulus of the material of the wire from these data.

Infinity Learn · Accepted Answer

$$y=F$$$$π$$$$r2$$×$$Le=50$$$$π$$$$0.050$$×$$10-222$$×$$1100.124$$×$$10-2=2.24$$×$$1011---(1)$$ Δ$$y=1.095$$×$$1010$$ $$N/m2$$Δ$$yy=2$$Δ$$rr+$$Δ$$ll+$$Δ$$ee=20.0010.05+0.1110+0.0010.125=0.0489$$ Δ$$y=0.0489$$×$$2.24$$×$$1011=1.09$$×$$1010$$  from (1)

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