A steel tape of 300 ~cm length is graduated at 27^ C . The length of a steel rod measured using the tape is found to be 110 ~cm at 50^ C . The actual length of steel rod at 50 ^ C is ( _ steel =1.2 10⁻⁵ ~K ⁻¹ )

Step-by-step solution

Let L^ be the length of steel rod. aligned & L ^ = L + L T & =300+300 1.2 10⁻⁵ (50-27) & =300+0.0828=300.0828 ~m aligned The actual length of steel rod at 50^ C is L ₂= 300.0828 300 110=110.03 ~cm