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 $2\times 10^{- 6} \,{}^\circ C^{- 1}$ , the period of the pendulum will have a 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

Answer: (D)

The fractional change in period
$\frac{\Delta T}{T}=\frac{1}{2}\alpha \Delta \theta $
$\frac{\Delta T}{T}=\frac{1}{2}\times 2\times 10^{- 6}\times 10=10^{- 5}$
% change in time period = $\frac{\Delta T}{T}\times 100=10^{- 5}\times 100=10^{- 3}$