Question

The pendulum of a clock is made of brass. If the clock keeps correct time at ${20}^{\circ }C$, how many seconds per day will it loose at ${35}^{\circ }C$? ($\alpha$ for brass = $1.8\times {10}^{-5}{/}^{\circ }C)$

• A. 12.96 s
• B. 1.29 s
• C. 129.6 s
• D. 8.64 s

Answer 1

The correct option is A 12.96 s

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

$\frac{\Delta T}{T}=\frac{1}{2}\times \frac{\Delta L}{L}=\frac{1}{2}\alpha \Delta \theta$

$\Delta T=\frac{T}{2}\alpha \Delta \theta$

${\alpha }_{Brass}=1.8\times {10}^{-5}{/}^{o}C$

$\Delta T=\frac{86400}{2}\times 1.8\times {10}^{-5}\times 15$

$\Delta T=12.96sec$