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QPages 12-14: Q34: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q34 Solution: A circular disc made of iron is rotated about its axis at a…

⚠️ Common Exam Traps & Conceptual Pitfalls

Students frequently take the fractional change $\Delta v/v = \alpha\Delta T$ and report it as the percent change, forgetting to multiply by 100; this turns a $3.6\times10^{-4}$ change into 0.036% instead of 0.036. Always convert the dimensionless ratio to a percentage by multiplying by 100.

A circular disc made of iron is rotated about its axis at a constant velocity ω\omega. Calculate the percentage change in the linear speed of a particle of the rim as the disc is slowly heated from 20�C to 50�C, keeping the angular velocity constant. Coefficient of linear expansion of iron = 1.2×10−5 �C−11.2 \times 10^{-5} \text{ �C}^{-1}.

Step-by-Step Verified Solution

**Answer:** Percentage change =0.036%= 0.036\% **Step-by-Step Explanation:** Linear speed v=ωrv = \omega r. Since ω\omega is constant, v∝rv \propto r. Δv/v=Δr/r=αΔT=1.2×10−5×30=3.6×10−4=0.036%\Delta v/v = \Delta r/r = \alpha \Delta T = 1.2 \times 10^{-5} \times 30 = 3.6 \times 10^{-4} = 0.036\%.

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