In order to determine the Young’s Modulus of a wire of radius $$0.2$$ cm (measured$$ using a scale of least $$count=0.001$$ $$cm) and length $$1m$$ (measured$$ using a scale of least $$count=1mm), a weight of mass $$1kg(measured$$ using a scale of least count $$=1$$ $$g)was$$ hanged to get the elongation of $$0.5$$ $$cm(measured$$ using scale of least count $$0.001$$ $$cm)$$.What will be the fractional error in the value of Young ‘s Modulus determined by this experiment?

Question

Infinity Learn · Accepted Answer

$$Y=mgL$$$$π$$$$r2e$$ ,  ⇒ dYY%$$=(dmm+dLL+2drr+dee)$$×$$100$$ ⇒ dYY%$$=$$[$$11000+11000+2(0.0010.2)+(0.0010.5)$$]×$$100$$  $$=1.4$$%

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