1.  Refer to Exercise 12. Estimate n, and find the relative uncertainty in the estimate, from the following measurements: θ1 = 0.216 ± 0.003 radians and θ2 = 0.456 ± 0.005 radians.

2.   Refer to Exercise 14. Assume that l = 10.0 cm ± 0.5% and d = 10.4 cm ± 0.5%.

a.  Estimate R, and find the relative uncertainty in the estimate. Does the relative uncertainty depend on k?

b.   Assume that either l or d can be remeasured with relative uncertainty 0.2%. Which should be remeasured to provide the greater improvement in the relative uncertainty of the resistance?

3.   Refer to Exercise 15. Assume that F = 750 ± 1 N, R = 0.65 ± 0.09 mm, L0 = 23.7 ± 0.2 mm, and L1 = 27.7 ± 0.2 mm. Estimate Y, and find the relative uncertainty in the estimate.