Question

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

• A. $2\times {10}^{-3}$
• B. $3\times {10}^{-3}$
• C. $4\times {10}^{-3}$
• D. $1\times {10}^{-3}$

Answer 1

The correct option is D $1\times {10}^{-3}$

Given:
Change in temperature, $\Delta \theta =10{}^{\circ }\text{C}$
Coefficient of linear expansion of rod, $\alpha =2\times {10}^{-6}/{}^{\circ }\text{C}$
To find:
Percentage change in time period, $\frac{\Delta T}{T}\times 100=?$
We know that,
Fractional change in time period is given by
$\frac{\Delta T}{T}=\frac{1}{2}\alpha \Delta \theta$
$=\frac{1}{2}\times 2\times {10}^{-6}\times 10={10}^{-5}$
Now, $\%$ change,
$=\frac{\Delta T}{T}\times 100={10}^{-5}\times 100={10}^{-3}\%$