Question

A strain gauge is to be used in measuring the strain on a test specimen. A strain gauge with an initial resistance of 100 ? exhibits a decrease of 0.12 The gage factor is 2.00. The initial length of the gage was 1.000 cm. What is most nearly the final length of the strain gage? a) 0.9992 cm b) 0.9994 cm c) 1.0005 cm d) 1.0050 cm

Answer 1

The most nearly the final length of the strain gageb) 0.9994 cm

Step-by-step explanation:

The strain gauge undergoes a deformation corresponding to the strain on the test specimen, causing a decrease in resistance. To find the final length, use the formula ΔR/R = GF * ε, where ΔR is the change in resistance, R is the initial resistance, GF is the gauge factor, and ε is the strain. Rearranging for strain, ε = ΔR / (GF * R), and substituting the given values, we get ε = -0.0012.

Now, using the formula for strain (ε = ΔL / L), where ΔL is the change in length and L is the initial length, rearrange for ΔL and substitute ε to find ΔL = -0.000012 cm. Finally, subtract ΔL from the initial length to get the final length, which is approximately 0.9994 cm.

The negative sign indicates a contraction in length due to compressive strain on the test specimen. The gage factor of 2.00 amplifies the strain's effect on resistance, resulting in a noticeable change in the strain gauge's length.

Therefore, the correct answer is: b) 0.9994 cm