$A$ pendulum clock keeps correct time at $0^{\circ}C$. If its mean coefficient of linear expansion is $\alpha /^{\circ}C$,what is the loss in seconds per day by the clock if the temperature rises by $t^{\circ}C$?

• A
  $\frac{\frac{1}{2}\alpha t \times 864000}{1 - \frac{\alpha t}{2}}$
• B
  $\frac{1}{2}\alpha t \times 86400$
• C
  $\frac{\frac{1}{2}\alpha t \times 86400}{(1 - \frac{\alpha t}{2})^2}$
• D
  $\frac{\frac{1}{2}\alpha t \times 86400}{1 + \frac{\alpha t}{2}}$