Question

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

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

Answer 1

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

We know that:$\frac{\Delta T}{T}=\frac{1}{2}a\Delta \theta$
Given:$\Delta \theta ={10}^{\circ }C,\alpha =2\times {10}^{-6}{/}^{\circ }C$
Fractional change in period
$\frac{\Delta T}{T}=\frac{1}{2}a\Delta \theta =\frac{1}{2}\times 2\times {10}^{-6}\times 10$
$\%change=\frac{\Delta T}{T}\times 100$
=${10}^{-5}\times 100$
=${10}^{-3}\%$

Final answer (d)