A hole is drilled in a metal sheet. At , the diameter of the hole is 5 cm. When the sheet is heated to , the change in the diameter of the hole is . The value of will be _______ if the coefficient of linear expansion of the metal is .

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Solution

Q.
A hole is drilled in a metal sheet. At $27 ° C$ , the diameter of the hole is 5 cm. When the sheet is heated to $177 ° C$ , the change in the diameter of the hole is $d \times 10^{- 3} cm$ . The value of $d$ will be _______ if the coefficient of linear expansion of the metal is $1.6 \times 10^{- 5} / ° C$ . [2023]

Ans.
(12)

$d_{0} at 27 ° C and d_{1} at 177 ° C$

$d_{1} = d_{0} (1 + α Δ T)$

$(d_{1} - d_{0}) = 5 \times 1.6 \times 10^{- 5} \times 150 cm = 12 \times 10^{- 3} cm$

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