Question

Find υ and the uncertainty in υ if

υ = (a – b) d 2 / (q √ T )

and a = (1.83 ± 0.01) m, b = (1.65 ± 0.01) m, d = (0.001 06 ± 0.000 03) m, q = (4.28 ± 0.05) s and

T = (3.7 ± 0.1) X 10 3 s.

Answer 1

$$u=\frac{(1.83-1.65)(0.00106)^2}{4.28\sqrt{3700}}=1.77\cdot10^{-10}\\ \frac{du}{u}=\frac{0.02}{1.83-1.65}+2\frac{0.00003}{0.00106}+\frac{0.05}{4.28}+0.5\frac{0.1}{3.7}=0.2$$