Q. A pendulum clock keeps correct time at $0℃$. Its mean coefficient of linear expansions is $\alpha/℃,$ then the loss in seconds per day by the clock if the temperature rises by $t℃$ is
A) $\frac{\frac{1}{2}\alpha t \times 864000}{1 - \frac{\alpha t}{2}}$
B) $\frac{1}{2}\alpha t \times 86400$
C) $\frac{\frac{1}{2}\alpha t \times 86400}{\left( 1 - \frac{\alpha t}{2} \right)^{2}}$
D) $\frac{\frac{1}{2}\alpha t \times 86400}{1 + \frac{\alpha t}{2}}$
Explanation
(b) Loss in time per second $\frac{\mathrm{\Delta}T}{T} = \frac{1}{2}\alpha\mathrm{\Delta}\theta = \frac{1}{2}\alpha(t - 0)$
$\Rightarrow$ loss in time per day
$\mathrm{\Delta}t = \left( \frac{1}{2}\alpha t \right)t = \frac{1}{2}\alpha t \times (24 \times 60 \times 60) = \frac{1}{2}\alpha t \times 86400$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.