Question #6c7ad

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Question #6c7ad

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Answer 1 · 2017-02-19T11:08:08

$1.74s$ , 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 $dl$ is change in length, $L_0$ is initial length, $α$ is Coefficient of linear expansion of the material of the object, $t_f and t_i$ are initial and final temperatures respectively.

Inserting given values and taking $alpha=2.22xx10^-5"^@C^-1$ we get
$dl = 0.75xx2.22xx10^-5 (42 - 25)$
$=>dl = 0.75xx2.22xx10^-5 (42 - 25)=0.000283m$
New length of pendulum's wire $=L_0+dl$ $=0.75+0.000283=0.750283m$

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

$T=2pisqrt(l/g)$
Where $l$ is length of pendulum and $g$ is acceleration due to gravity and $=9.81ms^-2$

$:. T_"new"=2pisqrt(0.750283/9.81)=1.74s$ , rounded to two decimal places

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Question #6c7ad

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