Question

Find the error percentage using the general method shown for both 2 sigma and 3 sigma

4) The acceleration of gravity is measured by a pendulum from the following equation. g=(4m2 L )/t2 where: L; length of pendulum = 98.9 ± t; period of pendulum-2.35 ± 0.03 sec on 2σ 0.4 cm on 2σ Using the General method, calculate % error in “g” prediction based on a) 2σ b) 3σ Ge Veral Melho

Answer 1

Of = (4 pi^2L) H^2 L = 98.9 plusminus 0.4 cm t = 2.35 plusminus 0.03 rec take log in eq^n lng = ln 4 pi^2 + ln L + ln t^2 take derivative delta/g = delta/L + 2 delta t/t percentage error (delta g/g) times 100% = squareroot (delta L/L)^2 + (2 delta t/t)^2 times 100% = squareroot (0.4/98.9)^2 + (2 times 0.03/2.35)^2 times 100 squareroot 4.05 times 10^-3 + 0.65 times 10^-3 times 100 = squareroot 46.9 times 10^-2 times 100 = 6.8%