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 cm. The value of will be __________ if coefficient of linear expansion of the metal is /°C.
Show answer and solution
Answer: 12
Solution
Using linear expansion, the change in diameter is:
ΔD = D₀ × α × ΔT = 5 × 1.6×10⁻⁵ × (177 - 27) = 5 × 1.6×10⁻⁵ × 150
= 5 × 24×10⁻⁴ = 120×10⁻⁴ = 12×10⁻³ cm
So d × 10⁻³ = 12 × 10⁻³, giving d = 12. Note: holes expand the same way as the material itself — the hole diameter scales exactly as if it were filled with the same metal.
ΔD = D₀ × α × ΔT = 5 × 1.6×10⁻⁵ × (177 - 27) = 5 × 1.6×10⁻⁵ × 150
= 5 × 24×10⁻⁴ = 120×10⁻⁴ = 12×10⁻³ cm
So d × 10⁻³ = 12 × 10⁻³, giving d = 12. Note: holes expand the same way as the material itself — the hole diameter scales exactly as if it were filled with the same metal.
[JEE Main 2023 · 24 Jan · Shift 1 · Paper-1(B.E./B. Tech.)]