A steel tape measures the length of a copper rod as 90 . 0 cm when both are at 10 ° C , the calibration temperature for the tape. What would be the tape reading for the length of the rod when both are at 30 ° C . Given, α for steel 1.2 × 10 - 5 ° C - 1 and α for copper is 1.7 × 10 - 5 ° C - 1 .

Step-by-step solution

As the steel tape is calibrated at 10 ° C , therefore, adjacent centimeter marks on the steel tape will be separated by a distance of l t = l 10 1 + α s ∆ T = ( 1 + α s 20 ) cm Length of copper rod at 30 ° C = 90 1 + α c 20 cm Therefore, number of centimeters read on the tape will be = 90 1 + α c 20 1 1 + α s 20 = 90 1 + 1.7 × 10 - 5 × 20 1 1 + 1.2 × 10 - 5 × 20 = 90 × 1.00034 1.00024 = 90.01 cm