Question

A pendulum clock keeps correct time at $0^{\circ} C$. Its mean coefficient of linear expansions is $\alpha^{/ \circ} C ,$ then the loss in time (in sec) per day by the clock if the temperature rises by $t ^{\circ} C$ is

• A. $\frac{\alpha t}{2}$
• B. $\frac{1}{2} \alpha t$
• C. $43200\, \alpha t$
• D. $ 86400\, \alpha t$

Answer 1

Answer: (C)

Loss in time per day, $\frac{\Delta T }{ T }$
$=\frac{1}{2} \alpha \Delta \theta \times 24 \times 60 \times 60$
$\therefore \frac{\Delta T }{ T }=\frac{1}{2} \alpha \Delta \theta \times 86400$
$=\frac{1}{2} \times \alpha t \times 86400$
$\frac{\Delta T }{ T }= \alpha t 43200$