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 second lost in a day
$\Delta t =\frac{1}{2}\alpha \Delta \theta\times86400$
The coefficient of linear expansion of metal pendulum
$\alpha=\frac{2\Delta t}{\Delta\theta\times86400}=\frac{2\times12.5}{25\times86400}$
$\alpha=\frac{1}{86400}/^{\circ}C$