In order to determine the Young's Modulus of a wire of radius 0 . 2   cm (measured using a scale of…

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?
  1. 0.14%
  2. 0.9%
  3. 9%
  4. 1.4%

Solution

Y=StressStrain=FLAl=mgLπR2l

ΔYY=Δmm+ΔLL+2ΔRR+Δll

ΔYY×100=10011000+11000+20.0010.2+0.0010.5

=110+110+1+15=1410=1.4%

Asked in: JEE Main 2021 (16 Mar Shift 2)

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