JEE Advanced2007PhysicsMathematics in PhysicsActual
A student performs an experiment to determine the 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 ~mm 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 ~mm . Take g=9.8 ~m / s ^2 (exact). The Young's
Options
- A(2.0 0.3) 10¹¹ ~N / m ^2
- B(2.0 0.2) 10¹¹ ~N / m ^2
- C(2.0 0.1) 10¹¹ ~N / m ^2
- D(2.0 0.05) 10¹¹ ~N / m ^2
Correct answer
B. (2.0 0.2) 10¹¹ ~N / m ^2
Step-by-step solution
aligned Y & = F L A l = 4 F L d^2 l & = (4)(1.0 9.8)(2) (0.4 10⁻³ )^2 (0.8 10⁻³ ) =20 10¹¹ ~N / m ^2 aligned Further Y Y =2 ( d d )+ ( l l ) aligned Y & = 2 ( d d )+ ( l l ) Y= 2 0.01 0.4 + 0.05 0.8 2.0 10¹¹ & =0.2 10¹¹ ~N / m ^2 or (Y+ Y)=(2+0.2) 10¹¹ ~N / m ^2 aligned The correct option is (b).