A student performs an experiment to determine they Young's modulus of a wire,exactly 2m 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 ±0.5mm at a load of exactly 1kg.The student also measures the diameter of the wire to be 0.4mm with an uncertainty of ±0.01 mm . Take g=9.8m/s2(exact).The Young's modulus obtained from the reading is
A.(2.0 ± 0.3) X 1011 N/m2
B.(2.0 ± 0.2) X 1011 N/m2
C.(2.0 ± 0.1) X 1011 N/m2
D.(2.0 ± 0.05) X 1011 N/m2
Im getting C..but thats not ans.
106L = 2m (exact)
x = 0.8mm ± 6.25%
M = 1kg (exact)
d = 0.4mm ± 2.5%
g = 9.8 m/s2 (exact)
Y = 4MgL/(xπd2)
= 2*1011 N/m2
percentage error in Y = %error in x + 2.0*%error in d = 6.25+5 = 11.25 %
So. uncertainty = 2.0*0.1125 *1011 = 0.2*1011 (taking into account sig figs)
So, (b).
btw IIT gave answer as either (a) or (b)
