Question

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10°C, and the coefficient of linear expansion of the metal of the rod is 2 × 10^–6 per °C, the period of the pendulum will have percentage increase of

• A. – 2 × 10^–3
• B. – 1 × 10^–3
• C. 2 × 10^–3
• D. 1 × 10^–3

Answer 1

Answer: (D)

1 × 10^–3

Answer 2

Fractional change in period

$\frac{\Delta T}{T} = \frac{1}{2}\alpha\Delta\theta = \frac{1}{2} \times 2 \times 10^{- 6} \times 10 = 10^{- 5}$

% change $= \frac{\Delta T}{T} \times 100 = 10^{- 5} \times 100 = 10^{- 3}\%$