Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is
The correct option is D. 8 : 1.
Given,
Outside pressure = 1 atm
Pressure inside first bubble = 1.01 atm
Pressure inside second bubble = 1.02 atm
Excess pressure △P1 = 1.01 - 1 = 0.01 atm
Excess pressure △P2 = 1.02 - 1 = 0.02 atm
We know that, △P=4Tr, where T is the surface tension and R is the radius of the bubble.
∴△P∝1r⇒r∝1△P⇒r1r2=△P2△P1=0.020.01=21
Since V=43πr3
∴V1V2=⟮r1r2⟯3=⟮21⟯3=81