A hole is drilled in a metal sheet. At 27, the diameter of hole is 5 cm. When the sheet is heated to 177, 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. Numerical answer type. Work it out, then open the answer.

Answer: 12. A hole expands like the material around it: Δ d = dαΔ T. Δ d = 5 × 1.6×10⁻⁵ × 150 = 0.012 cm 0.012 = 12×10⁻³ cm, so d = 12.

A hole is drilled in a metal sheet. At 27, the diameter of hole is 5… | JEE Main 2023 (24 Jan, Shift 1)

Q40JEE Main 2023 · 24 JAN · SHIFT 1Medium

Thermometry & Thermal Expansion

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

Numerical answer type. Work it out, then open the answer.

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Answer: 12

A hole expands like the material around it: $\Delta d = d\alpha\Delta T$ .
$\Delta d = 5 \times 1.6\times10^{-5} \times 150 = 0.012$ cm
$0.012 = 12\times10^{-3}$ cm, so $d = 12$ .

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Thermometry & Thermal Expansion question from JEE Main 2023 (24 Jan, Shift 1)

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