Question

A clock pendulum made of invar has a period of $0.5s$, at $20^{\circ }C$. If the clock is used in a climate where the temperature averages to $30^{\circ }C$, how much time does the clock lose in each oscillation? (For invar, $\alpha =9\times 10^{-7}/{}^{\circ }C$, $g=$ constant $)$

• A. $2.25\times 10^{-6}s$
• B. $2.5\times 10^{-7}s$
• C. $5\times 10^{-7}s$
• D. $1.125\times 10^{-6}s$

Answer 1

Answer: (C)

Time period of oscillation
$T=2\pi \sqrt{\frac{l}{g}}$
$\frac{dT}{T}=\frac{1}{2}\frac{dl}{l}$
As, $\frac{dl}{l}=\alpha dt$
$\Rightarrow \frac{dT}{T}=\frac{1}{2}\alpha dt$
$=\frac{1}{2}\times 9\times 10^{-7}\times (30-20)$
$=4.5\times 10^{-6}$
$\therefore$ Loss in time $=4.5\times 10^{-6}\times 0.5$
$=2.25\times 10^{-6}s$