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 = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1g) 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?
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 = 1 mm), a weight of mass 1 kg (measured using a scale of least count = 1g) 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?
Option 1 -
9%
Option 2 -
0.9%
Option 3 -
0.14%
Option 4 -
1.4%
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1 Answer
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Correct Option - 4
Detailed Solution:using hook's law:
σ = Yε ⇒ f/A = Y (x/l) ⇒ Y = fl/ (xA) = fl/ (xπr²)
Using error analysis formula:
ΔY/Y = Δf/f + Δl/l + Δx/x + 2Δr/r
%error in Y = [ (Δm/m) + (Δl/l) + (Δx/x) + 2 (Δr/r) ] × 100
= [ (1/1000) + (1/1000) + (0.001/0.5) + 2 (0.001/0.2) ] × 100
= [ 0.001 + 0.001 + 0.002 + 0.01 ] × 100 = 1.4%
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