A metal rod of length L at temperature T₀ is heated to temperature T. If α is the coefficient of linear expansion, the new length is: MCQ with Answer and Explanation
A metal rod of length L at temperature T₀ is heated to temperature T. If α is the coefficient of linear expansion, the new length is:
A. Lα(T - T₀)
B. L(1 + αT)
C. L(1 + αT₀)
D. L[1 + α(T - T₀)]
Answer: Option D
Solution (By JKSSB Mock Tests)
Linear expansion formula: ΔL = L₀αΔT, where ΔT = T - T₀. Thus new length L' = L₀ + ΔL = L₀[1 + α(T - T₀)]. Option A incorrectly uses absolute temperature T instead of temperature change. Option C gives only the change, not total length. Option D uses initial temperature incorrectly. Memory aid: 'Expansion depends on temperature change, not absolute value'. This standard formula application is common in thermal physics questions. Always identify initial length and temperature reference point to avoid sign errors.
Explanation:
T = 2π√(l/g): depends on l and g, independent of mass (gravitational and inertial mass cancel). Memory aid: 'Pendulum: T ∝ √(l/g); independent of mass for small angles'. Oscillations concept frequently tested in competitive exams.
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