# Question 6c7ad

Feb 19, 2017

$1.74 s$, rounded to two decimal places

#### Explanation:

The linear thermal expansion of an object can be expressed as

dl = L_0 α (t_f - t_i)
where $\mathrm{dl}$ is change in length, ${L}_{0}$ is initial length, α is Coefficient of linear expansion of the material of the object, ${t}_{f} \mathmr{and} {t}_{i}$ are initial and final temperatures respectively.

Inserting given values and taking alpha=2.22xx10^-5"^@C^-1# we get
$\mathrm{dl} = 0.75 \times 2.22 \times {10}^{-} 5 \left(42 - 25\right)$
$\implies \mathrm{dl} = 0.75 \times 2.22 \times {10}^{-} 5 \left(42 - 25\right) = 0.000283 m$
New length of pendulum's wire$= {L}_{0} + \mathrm{dl}$ $= 0.75 + 0.000283 = 0.750283 m$

Time period $T$ of a simple pendulum is given by

$T = 2 \pi \sqrt{\frac{l}{g}}$
Where $l$ is length of pendulum and $g$ is acceleration due to gravity and $= 9.81 m {s}^{-} 2$

$\therefore {T}_{\text{new}} = 2 \pi \sqrt{\frac{0.750283}{9.81}} = 1.74 s$, rounded to two decimal places