A student performs an experiment to determine young's modulus of a wire, exactly 2 m long, by searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0 . 8 mm with an uncertainty of ± 0.05 m m at a load of exactly 1 . 0 kg . The student also measures the diameter of the wire to be 0 . 4 mm with an uncertainty of ± 0.01 m m . The young's modulus obtained from the reading is [ Take g = 9 .8 ms - 2 ]

Question

A student performs an experiment to determine young's modulus of a wire, exactly 2 m long, by searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0 . 8 mm with an uncertainty of ± 0.05 m m at a load of exactly 1 . 0 kg . The student also measures the diameter of the wire to be 0 . 4 mm with an uncertainty of ± 0.01 m m . The young's modulus obtained from the reading is [ Take g = 9 .8 ms - 2 ], 2 .0 ± 0 .3 × 10 11 Nm - 2, 2 .0 ± 0 .2 × 10 11 Nm - 2, 2 . 0 ± 0 .1 × 10 11 Nm - 2, 2 .0 ± 0 .05 × 10 11 Nm - 2

MARKS App · Accepted Answer

Young's modulus Y = F L A l = 4 F L π d 2 l = 4 1.0 × 9.8 2 π 0.4 × 10 - 3 2 0.8 × 10 - 3 = 2.0 × 10 11 N m - 2 Further, ∆ Y Y = 2 ∆ d d + ∆ l l ∴ ∆ Y = 2 ∆ d d + ∆ l l Y = 2 × 0.01 0.4 + 0.05 0.8 × 2.0 × 10 11 = 0.2 × 10 11 N m - 2 Or Y + ∆ Y = 2 + 0.2 × 10 11 N m - 2

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