More practice questions

4. Q4. A pendulum clock with a brass pendulum (α_l = 1.8 × 10^⁻⁵ K^⁻¹) keeps correct time at 20 °C. At 40 °C, about how many seconds a day does it lose? (The period is proportional to the square root of the length.)

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   The length grows by the fraction α_lΔT = 3.6 × 10^⁻⁴, so the period grows by half of that, 1.8 × 10^⁻⁴. In a day of 86 400 s the clock loses about 1.8 × 10^⁻⁴ × 86 400, about 15.5 s (roughly 16 s). A longer period means fewer swings a day, so the clock runs slow.

5. Q5. A bimetallic strip is made of brass and iron riveted together. Which way does it bend when heated, and why?

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   Brass (α_l = 1.8 × 10^⁻⁵ K^⁻¹) expands more than iron (1.2 × 10^⁻⁵ K^⁻¹), so the strip bends with the brass on the outside of the curve. Such strips are used in thermostats.

6. Q6. A copper rod is clamped between two rigid walls and heated by 20 °C. Find the thermal stress. Take Y = 1.1 × 10^¹¹ N m^⁻² and α_l = 1.7 × 10^⁻⁵ K^⁻¹ (NCERT Tables 8.1 and 10.1).

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   Stress = Yα_lΔT = 1.1 × 10^¹¹ × 1.7 × 10^⁻⁵ × 20, about 3.7 × 10^⁷ N m^⁻².