A thin copper wire of length ℓ increases in length by 1% when heated from 20°C to 70°C. If a thin copper plate of length 3ℓ and breadth 2ℓ is heated from 20°C to 70°C, the percentage increase in its area will be :
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When a material is heated, its linear expansion is given by ΔL = αLΔT, where α is the coefficient of linear expansion. For the wire, a 1% increase in length means ΔL/L = 0.01 = α(50°C). Therefore, α = 0.01/50 = 0.0002 per °C.
For a 2D area, the area expansion coefficient is 2α. The original plate area is A0 = (3ℓ)(2ℓ) = 6ℓ2. The percentage increase in area is given by (ΔA/A0) × 100% = (2αΔT) × 100%.
Substituting the values: (2 × 0.0002 × 50) × 100% = (0.02) × 100% = 2%.
Final Answer: 2%