In an experiment of determine the Young's modulus of wire of a length exactly 1 m , the extension in the length of the wire is measured as 0 . 4 mm with an uncertainty of ± 0 . 02 mm when a load of 1 kg is applied. The diameter of the wire is measured as 0 . 4 mm with an uncertainty of ± 0 . 01 mm . The error in the measurement of Young's modulus Δ Y is found to be x × 10 10 N m - 2 . The

Step-by-step solution

Given here, Length, L = 1   m and extension in length, Δ L = 0 . 4 × 10 - 3   m Mass of load, m = 1   kg and diameter of wire, d = 0 . 4 × 10 - 3   m Young's modulus is given by Y = F L A Δ L = m g × 1 π d 2 4 0 . 4 × 10 - 3 ⇒ Y = 10 × 4 π 0 . 4 × 10 - 3 2 × 0 . 4 × 10 - 3 ⇒ Y = 40 × 7 22 × 64 × 10 - 3 × 10 - 9 ⇒ Y = 0 . 199 × 10 - 12   N   m - 2 Error in measurement of Young'