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  4. A metal rod is used as a bar pendulum. If the room temperature rise by 10° C and coefficient of linear expansion of the metal of the rod is 3 × 10-5 per ° C , the period of pendulum will have percentage increases of

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Q. A metal rod is used as a bar pendulum. If the room temperature rise by $10^{\circ} C$ and coefficient of linear expansion of the metal of the rod is $3 \times 10^{-5}$ per $^{\circ} C ,$ the period of pendulum will have percentage increases of

Thermal Properties of Matter

Solution:

$\frac{\Delta T }{ T }=\frac{1}{2} \alpha \Delta \theta=\frac{1}{2} \times 3 \times 10^{-5} \times 10=15 \times 10^{-5}$
$\%$ increase $=\frac{\Delta T }{ T } \times 100$
$=15 \times 10^{-5} \times 100$
$=15 \times 10^{-3}=0.015 \%$