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 1 m (measured using a scale of least count = 1 mm ), a weig

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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 1 m (measured using a scale of least count = 1 mm ), a weight of mass 1 kg (measured using a scale of least count = 1 g ) was hanged to get the elongation of 0 . 5 cm (measured using a scale of least count 0 . 001 cm ). What will be the fractional error in the value of Young's Modulus determined by this experiment?

TestHub · Accepted Answer

Y = Stress Strain = F L A l = m g L π R 2 l Δ Y Y = Δ m m + Δ L L + 2 Δ R R + Δl l Δ Y Y × 100 = 100 1 1000 + 1 1000 + 2 0 . 001 0 . 2 + 0 . 001 0 . 5 = 1 10 + 1 10 + 1 + 1 5 = 14 10 = 1 . 4 %

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