Answer:
It will take 12 hours to settle out same particulate with half the diameter from same chimney.
Explanation:
The settling rate of particulates = S
Diameter of the particulate = d
[tex]S\propto d^2[/tex]
The settling rate of one type of particulates = [tex]S_1[/tex]
Diameter of the one type of particulate = [tex]d_1[/tex]
The settling rate of other type of particulates = [tex]S_2[/tex]
Diameter of the other type of particulate = [tex]d_2=0.5d_1[/tex]
[tex]\frac{S_1}{(d_1)^2}=\frac{S_2}{(d_2)^2}[/tex]
[tex]\frac{S_1}{(d_1)^2}=\frac{S_2}{(0.5d_1)^2}[/tex]
[tex]S_1=4S_2[/tex]
[tex]S_2=\frac{S_1}{4}[/tex]
Given that settling of one type of particulate from chimney is 2 days.So settling of other type of particulate from same chimney:
[tex]S_2=\frac{2 days}{4}=0.5 days[/tex]
1 day = 24 hours
0.5 days = 0.5 × 24 hours = 12 hours
It will take 12 hours to settle out same particulate with half the diameter from same chimney.
