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 of pendulum is

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

. .

We know that,

Loss of time due to heating a pendulum is given as $\Delta T$ = $\frac{1}{2}\alpha \Delta \theta T$

where

$△T$ = change in time

$\alpha$ = coefficient of linear expansion of metal of pendulum

$△\theta$ = change in temperature

$T$ = total time

$\Rightarrow$ $12.5$ = $\frac{1}{2}\times \alpha \times (25-0{)}^{\circ }C\times 86400$

(Since 24 hr = 86400 seconds)

$\Rightarrow$ $\alpha$ = $\frac{1}{86400}$ ${/}^{\circ }C$.