Please see attachment for problems with appropriate symbol notations.
6. Let I = 1/2 M(R^2 + r^2). What is the equation for sigma_I, if M, R and r are measured quantities? If we require delta_I/I = 0.1%, what is the relative precisionfor the measurements of M, R and r? (Suppose that R = alpha*r, alpha> 1, and delta_R = delta_r.)
7. The voltageV along a transmission line is V(x) = V0 exp(-x/x_a), where x is the position along the line. Find x_a and its uncertainty sigma_x_a measuring V0, V and x. Find the best value of V0, which minimizes sigma_x_a.
8. The angle variation theta of a wheel rotating under a constant acceleration, is measured at different times t. A plot of t^2 vs. theta of the datais fitted with a straight line y = a + bx. Supposing that the initial angular velocitywas zero, what are a and b? What is the value of sigma_(t^2) for t = (1.32 +- 0.02) s?
This solution solves three problems involving the propagation of measurement errors. All steps are show with brief justifications.