Question

A clock which keeps correct time at ${20}^{\circ }C$ is subjected to ${40}^{\circ }C$. If coefficient of linear expansion of pendulum is $12\times {10}^{-6}{/}^{\circ }C$. How much will it gain or lose in time

• A. $10.3\sec /day$
• B. $20.6\sec /day$
• C. $5\sec /day$
• D. $20min/day$

Answer 1

Answer: (B)

$20.6\sec /day$

Time period $T\propto \sqrt{l}$

$\Rightarrow \frac{△T}{T}=\frac{1}{2}\frac{△l}{l}=\frac{1}{2}\alpha △\theta$

$=\frac{1}{2}\times 12\times {10}^{-6}\times (40-20)=12\times {10}^{-5}$

$\Rightarrow △T=12\times {10}^{-5}\times 86400seconds/day$

$△T\approx 10.3seconds/day$