A pendulum clock having copper rod keeps correct time at  20^oC.It gains 15 s per day if cooled to 0^oC. The coefficient of linear expansion of copper is

$\frac{{\mathrm{T}}_{20}-{\mathrm{T}}_0}{{\mathrm{T}}_0}=\frac{1}{2}\times \mathrm{\alpha }\times 20=10\mathrm{\alpha }$

Here T₂₀ is the correct time period. The time period at 0^oC is smaller so that the clock runs fast. The time gained in 24h.

  $\begin{array}{l} =24\mathrm{h}\times \mathrm{\alpha }\times 10\\ \Rightarrow 15\mathrm{s}=24\mathrm{h}\times \mathrm{\alpha }\times 10\\ \mathrm{\alpha }=\frac{15\mathrm{s}}{86400\mathrm{s}\times {10}^{\circ }\mathrm{C}}=1.7\times {10}^{-5}{/}^{\circ }\mathrm{C}\end{array}$