Question

A clock with a metal pendulum beating seconds keeps correct time at $0^{\circ} C$. If it loses $12.5\, s$ a day at $25^{\circ} C$, the coefficient of linear expansion of metal pendulum is

• A. $\frac{1}{86400} /{ }^{\circ} C$
• B. $\frac{1}{43200} /{ }^{\circ} C$
• C. $\frac{1}{14400} /{ }^{\circ} C$
• D. $\frac{1}{28800} /{ }^{\circ} C$

Answer 1

Answer: (A)

Number of seconds lost in a day
$\Delta t=\frac{1}{2} \alpha \Delta \theta \times 86400$
The coefficient of linear expansion of metal pendulum
$\alpha=\frac{2 \Delta t}{\Delta \theta \times 86400}=\frac{2 \times 12.5}{25 \times 86400}$
$\alpha=\frac{1}{86400} /{ }^{\circ} C$