NTA Abhyas JEE Main2020PhysicsUnits and DimensionsPractice
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 uncert
Options
- A2 .0 ± 0 .3 × 10 11   Nm - 2
- B2 .0 ± 0 .2 × 10 11   Nm - 2
- C2 . 0 ± 0 .1 × 10 11   Nm - 2
- D2 .0 ± 0 .05 × 10 11   Nm - 2
Correct answer
B. 2 .0 ± 0 .2 × 10 11   Nm - 2
Step-by-step solution
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