Question

A pendulum clock keeps correct time at 0°C. Its mean coefficient of linear expansions is $\alpha/{^\circ}C$, then the loss in seconds per day by the clock if the temperature rises by t°C 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. $\frac{\frac{1}{2}\alpha t \times 86400}{1 + \frac{\alpha t}{2}}$

Answer 1

Answer: (B)

$\frac{1}{2}\alpha t \times 86400$

Answer 2

Loss in time per second $\frac{\Delta T}{T} = \frac{1}{2}\alpha\Delta\theta = \frac{1}{2}\alpha(t - 0)$

⇒ loss in time per day

$\Delta t = \left( \frac{1}{2}\alpha t \right)t = \frac{1}{2}\alpha t \times (24 \times 60 \times 60) = \frac{1}{2}\alpha t \times 86400$