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 _____,

Question

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 ∘

TestHub · Accepted Answer

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

$\Rightarrow d^{'} - d_{0} = (5) \times (1.6 \times 10^{- 5}) \times (177 - 27)$

$= 12 \times 10^{- 3} cm$

Hence, required value of $d = 12$ .

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