1.  A cylindrical hole is bored through a steel block, and a cylindrical piston is machined to fit into the hole. The diameter of the hole is 20.00 ± 0.01 cm, and the diameter of the piston is 19.90 ± 0.02 cm. The clearance is one-half the difference between the diameters. Estimate the clearance and find the uncertainty in the estimate.

2.   A force of F = 2.2 ± 0.1 N is applied to a block for a period of time, during which the block moves a distance d = 3 m, which is measured with negligible uncertainty. The work W is given by W = Fd. Estimate W, and find the uncertainty in the estimate.

3.   The specific gravity of a substance is given by G = DS /DW, where DS is the density of the substance in kg/m3 and DW is the density of water, which is known to be 1000 kg/m3 . The density of a particular substance is measured to be DS = 500 ± 5 kg/m3 . Estimate the specific gravity, and find the uncertainty in the estimate.