First slide

Thermal expansion

Question

A uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{0} C,$ and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{- 6} per^{0} C$ , the period of the pendulum will have percentage increase of

Moderate

A

$- 2 \times 10^{- 3}$
B

$- 1 \times 10^{- 3}$
C

$2 \times 10^{- 3}$
D

$1 \times 10^{- 3}$

Solution

Fractional change in period
$\frac{∆ T}{T} = \frac{1}{2} α ∆ θ = \frac{1}{2} \times 2 \times 10^{- 6} \times 10 = 10^{- 5}$
$% change = \frac{∆ T}{T} \times 100 = 10^{- 5} \times 100 = 10^{- 3} %$

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