The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least count 0.1 cm is 150 cm. When a weight of 100 N is applied to the wire, the extension in length is 0.5 cm, measured by a micrometer of least count 0.001 cm. The error in the measured Young's modulus is 10^9 N/m ^2 . The value of is _______. (Ignore the contribution of the load to Young's modulus

Step-by-step solution

The formula for Young's modulus is given by: Y = F L₀ A L = 4 F L₀ d^2 L Substituting the given values into the formula: Y = 4 100 1.5 (0.08 10⁻²)^2 (0.5 10⁻²) Y = 600 64 10⁻⁸ 5 10⁻³ = 15 8 10¹¹ N/m ^2 The relative error in Young's modulus is: Y Y = L₀ L₀ + 2 d d + ( L) L Substituting the least counts as absolute errors and the measured values: Y Y = 0.1 150 + 2 0.001 0.08 + 0.001 0.5 Y Y = 1 1500 + 1 40 + 1 500 Y Y = 2 + 75 + 6 3000 = 83 3000 The absolute error in Young's modulus is: Y = Y Y Y = ( 15 8 10¹¹ ) 83 3