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, $a = 9 \times 10^{-7} /^{\circ} C, g$ = 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

The Correct Option is A

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