Question

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

• A. - 2 X 10^-3
• B. - 1 X 10^-3
• C. 2 X 10^-3
• D. 1 X10^-3

Answer 1

The correct option is D

1 X10^-3

Fractional change in period
$\frac{△T}{T}=\frac{1}{2}\alpha △\theta =\frac{1}{2}\times 2\times {10}^{-6}\times 10={10}^{-5}$
$\%change=\frac{△T}{T}\times 100={10}^{-5}\times 100={10}^{-3}\%$