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  • A uniform metal rod is used as a bar pendulum. If the room temperature rises by <img alt="10^{\circ} \mathrm{C}" src="https://entrancecorner.oncodecogs.com/gif.latex?10%5E%7B%5Ccirc%7D%20%5Cmathrm%

A uniform metal rod is used as a bar pendulum. If the room temperature rises by 10^{\circ} \mathrm{C}, and the coefficient of linear expansion of the metal is 2 \times 10^{-6}\text{~ per~} ^{\circ} \mathrm{C} the period of a pendulum will have percentage increase of

Option: 1

-2 \times 10^{-3}


Option: 2

-1 \times 10^{-3}


Option: 3

2 \times 10^{-3}


Option: 4

1 \times 10^{-3}


Answers (1)

best_answer

The fractional change in period,

\begin{aligned} \frac{\Delta T}{T} & =\frac{1}{2} \alpha \Delta Q \\ & =\frac{1}{2} \times 2 \times 10^{-6} \times 10=10^{-5} \end{aligned}\\ \begin{aligned} \% \text { change } & =\frac{\Delta T}{T} \times 100 \\ & =10^{-5} \times 100=10^{-3} \% \end{aligned}
 

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Nehul

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