Question

A clock pendulum made of invar has a period of $0.5 \,s$, 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}} $
$\frac{d T}{T} =\frac{1}{2} \frac{d l}{l}$
As, $ \frac{d l}{l} =\alpha d t $
$\Rightarrow \frac{d T}{T} =\frac{1}{2} \alpha d t $
$=\frac{1}{2} \times 9 \times 10^{-7} \times(30-20) $
$=4.5 \times 10^{-6}$
$\therefore $ Loss in time $=4.5 \times 10^{-6} \times 0.5$
$=2.25 \times 10^{-6} s$