A hole is drilled in a metal sheet. At 27 ° C , the diameter of hole is 5 cm . When the sheet is heated to 177 ° C , the change in the diameter of hole is d × 10 - 3 cm . The value of d will be _____, if coefficient of linear expansion of the metal is 1 . 6 × 10 - 5 / C ∘

Step-by-step solution

Expansion of hole will be similar to that of an imaginary disc. Let diameter be d 0 at 27   ° C and d ' at 177   ° C . Therefore, we can write d ' = d 0 1 + α Δ T Therefore, change in diameter will be ⇒ d ' - d 0 = 5 × 1 . 6 × 10 - 5 × 177 - 27 = 12 × 10 - 3   cm Hence, required value of d = 12 .