Question #6c7ad

1 Answer
Feb 19, 2017

#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