Question

A clock pendulum made of invar has a period of $0.5sec$ at ${20}^{o}C$. If the clock is used in a climate where average temperature is ${30}^{o}C$, approximately. How much slow $\left(insec\right)$ will the clock run in ${10}^{6}sec$. (Given: ${\alpha }_{invar}=1\times {10}^{-6}{/}^{o}C$)

Answer 1

$T=2\pi \sqrt{\frac{l_0}{g}}$

$T^{\prime }=2\pi \sqrt{\frac{l_0(1+\alpha t)}{g}}$

$⟹\Delta T=\frac{1}{2}\alpha t\times T$

$=\frac{1}{2}\times {10}^{-6}\times 10\times {10}^{6}s=5s$