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  4. 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.

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

JEE MainJEE Main 2023Thermal Properties of Matter

Solution:

$d _0$ at $27^{\circ} C \,\& \,d _1$ at $177^{\circ} C$
$ d _1= d _0(1+\alpha \Delta T )$
$d _1- d _0=5 \times 1.6 \times 10^{-5} \times 150 \,cm$
$ =12 \times 10^{-3} cm$