Question

Question #6c7ad

Answer 1

`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