A clock pendulum having coefficient of linear expansion =9 10^ -7… - Vidyadip

MCQ

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

A
$25 \times 10^{-7} s$
B
$5 \times 10^{-7} s$
C
$1.125 \times 10^{-6} s$
✓
$2.25 \times 10^{-6} s$

✓

Answer

Correct option: D.

$2.25 \times 10^{-6} s$

(d) : Given, coefficient of linear expansion $(\alpha)$ $=9 \times 10^{-7} /{ }^{\circ} C$
Change in temperature $(\Delta \theta)=30^{\circ} C -20^{\circ} C =10^{\circ} C$
If time period of the clock was $0.5 s$ at $20^{\circ} C$, then time lost by the clock in each oscillation is,
$
\begin{gathered}
{\left[T=2 \pi \sqrt{\frac{l}{g}} \text { taking and differentiation on both sides }\right]} \\
\Delta T=\frac{1}{2} \alpha \Delta \theta T \\
\Delta T=\frac{1}{2} \times 9 \times 10^{-7} \times 10 \times 0.5=2.25 \times 10^{-6} s
\end{gathered}
$

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