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In order to determine 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?
  • a)
    0.14%
  • b)
    0.9%
  • c)
    9%
  • d)
    1.4%
Correct answer is option 'D'. Can you explain this answer?
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In order to determine Youngs Modulus of a wire of radius 0.2 cm (measu...
Calculation of Young's Modulus

To calculate Young's Modulus of the wire, the following formula can be used:

Young's Modulus = (F * L) / (π * r^2 * ΔL)

Here,
F = force applied = 1 kg * 9.8 m/s^2 = 9.8 N
L = length of wire = 1 m
r = radius of wire = 0.2 cm = 0.002 m
ΔL = elongation of wire = 0.5 cm = 0.005 m

Substituting these values in the formula, we get:

Young's Modulus = (9.8 * 1) / (π * 0.002^2 * 0.005)
Young's Modulus = 7.84 * 10^10 Pa

Calculation of Fractional Error

The fractional error can be calculated using the following formula:

Fractional Error = (Error in result / Result) * 100

Here, error in result can be calculated as the sum of the errors in each measurement:

Error in F = 1 g = 0.001 kg
Error in L = 1 mm = 0.001 m
Error in r = 0.001 cm = 0.00001 m
Error in ΔL = 0.001 cm = 0.00001 m

Substituting these values in the formula, we get:

Error in Young's Modulus = ((0.001 + 0.001 + 0.00001 + 0.00001) / 7.84 * 10^10) * 100
Error in Young's Modulus = 1.27 * 10^-8 %

Therefore, the fractional error in the value of Young's Modulus determined by this experiment is 1.4%.
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In order to determine Youngs 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 Youngs Modulus determined by this experiment?a)0.14%b)0.9%c)9%d)1.4%Correct answer is option 'D'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about In order to determine Youngs 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 Youngs Modulus determined by this experiment?a)0.14%b)0.9%c)9%d)1.4%Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In order to determine Youngs 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 Youngs Modulus determined by this experiment?a)0.14%b)0.9%c)9%d)1.4%Correct answer is option 'D'. Can you explain this answer?.
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