Question

A student performs an experiment to determine the Young's modulus of a wire, exactly2m long, by Searle's method. In a partcular reading, the student measures the extension in the length of the wire to be 0.8mm with an uncertainty of +- 0.05mm at a load of exactly 1.0kg, the student also measures the diameter of the wire to be 04mm with an uncertainty of +-0.01mm. Take g=9.8m//s^(2) (exact). the Young's modulus obtained from the reading is

Answer 1

Young's modulus (Y) is= (2.00+.2)*10^11

As Y=4mgL/πd^2(uncertainty)

Hence on solving y=2*10^11

Error:Y(2∆d/d+∆l/l)

+.2*10^11

Hence Y=(2+.2)10^11

Answer 2

Here is your answer:

Explanation:

We know that

Y= mg/π(D^2/)4   x L/ l

ΔY/Y = 2ΔD/D+Δl/l

[ since the values of m,g,and L are exact]

so

=2 x 0.01/0.4+0.05/0.8

=2×0.025+0.0625  

=0.05+0.0625

=0.1125

ΔY=2×10^11×0.1125

=0.225×10^11