JAMB 2019 Physics · Question 34
A metal rod has a length of 100cm at 200 ^oC . At what temperature will its length be 99.4cm. If the linear…
Question
A metal rod has a length of 100cm at 200. At what temperature will its length be 99.4cm. If the linear expansivity of the material of the rod is 2 x 10
- A.200C
- B.300C
- C.100C
- D.-100C
Answer: D. -100C
Explanation written with AI and checked against the answer key
Analyze the question: A rod is 100 cm long at 200°C. It contracts to 99.4 cm as it cools. We need the temperature at which this happens, given α = 2 × 10⁻⁵ °C⁻¹. Concept: Linear expansivity is defined by α = ΔL / (L₁ × Δθ) so the change in length is ΔL = L₁ α Δθ. Solution: Change in length: ΔL = 99.4 − 100 = −0.6 cm Taking the original length as L₁ = 100 cm: Δθ = ΔL / (L₁ α) Δθ = −0.6 / (100 × 2 × 10⁻⁵) Δθ = −0.6 / (2 × 10⁻³) Δθ = −300 °C New temperature = 200 − 300 = −100 °C Check: Cooling by 300 °C gives a contraction of 100 × 2×10⁻⁵ × 300 = 0.6 cm, so the length is 99.4 cm. ✓ Tip: When a question gives a smaller length, the rod has been cooled, so the temperature change is negative. Always subtract it from the starting temperature. Also, a negative Celsius answer is perfectly possible, so don't reject it just because it looks unusual. The exam setters often use this to catch students out.AI can make mistakes. Report anything that looks wrong.
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