Q. A uniform metal rod is used as a bar pendulum. If the room temperature rise by 10$℃\ $ and coefficient of linear expansion of the metal of the rod is 2$\times 10^{6}\ ℃^{- 1}$, the period of pendulum will increase by
A) $1\ \times 10^{- 3}\%$
B) $- 1\ \times 10^{- 3}\%$
C) $2 \times 10^{- 3}\%$
D) $- 2\ \ \times 10^{- 3}\%$
Explanation
(a) From $T = 2\pi\sqrt{\frac{1}{g}}$
$\frac{\mathrm{\Delta}T}{T} = \frac{1}{2}\frac{\mathrm{\Delta}l}{l} = \frac{\alpha\mathrm{\Delta}T}{2}$
=$\frac{1}{2}\ \times 2 \times 10^{- 6} \times 10 = 10^{- 3}\%$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.