Question

A clock with an iron pendulum keeps correct time at $15^{\circ} C$. If the room temperature rises to $20^{\circ} C$ , the error in seconds per day will be (coefficient of linear expansion for iron is $0.000012/^{\circ} C$ )

• A. 2.5sec
• B. 2.6sec
• C. 2.4sec
• D. 2.2sec

Answer 1

Answer: (B)

2.6sec

Answer 2

$T =2 \pi \sqrt{\frac{1}{ g }}$ $\therefore \frac{\Delta T }{ T }=\frac{ R \pi}{\sqrt{ g }} \times \frac{1}{2 \sqrt{1}} \frac{\Delta l }{1}$ $\frac{\Delta T }{ T }=\frac{\pi}{\sqrt{ lg }} \alpha \Delta \theta$ $\Delta T =\frac{\pi a}{\sqrt{ lg }} \Delta \theta \times 2 \pi \times \sqrt{\frac{1}{ g }}=\frac{4 \pi^{2} \alpha \Delta \theta}{9} \times 24 \times 60 \times 60$ $\therefore \Delta T \approx 2 \cdot 6 sec$