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 students 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 1kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of +/-0.01 mm.The Young’s modulus obtained from the reading is (g= 9.8 ms−2)
Y=4Flπ D2△ l
=4 ×(1X9.8)X2(227)(0.4×10−3)2X(0.8X10−3)
=2×1011N m−2
Fractional error in y is
△ yy=+/−(2△ DD+△ ll)
or △ y =+/−(2 X0.010.4+0.050.8)×2×1011
=+/−0.2 × 1011Nm−2
Therefore y=(2× 1011+/−0.2 × 1011)N m−2