length of the wire L=2.890m D=0.82cm mass of suspended wire M=3kg extension in length of wire l=0.087cm calculate maximum possible error value wire
Answers
Consider a wire of length L and diameter d. Let length L increases by an amount l when wire is pulled by a longitudinal force F. The Young's modulus of the material of a wire is given by,
Y=StressStrain=F/Al/L=4FLπd2l.
In Searle's method, the parameters L is measured by a scale, d is measured by a screw gauge, l is measured by a Micrometer or Vernier scale, and F is specified weight. Differentiate the expression for Y to get the error in measured Y,
ΔYY=ΔLL+2Δdd+Δll,
where ΔL, Δd, and Δl are errors in measurement of L, d, and l, respectively. Generally, these errors are given by least count of the measuring instrument. The Searle's method is popular in IIT JEE because it test students understanding on (1) measurement using the screw gauge and the Micrometer/Vernier scale and (2) measurement error analysis. Given below are few problems asked in IIT-JEE.