Correct Answer - B
As mass of the air is conserved,
`therefore " " n_(1)+n_(2)=n " " ("as" pV=nRT)`
`therefore (p_(1)V_(1))/(RT_(1))+(p_(2)V_(2))/(RT_(2))=(pV)/(RT)`
As temperature is constant,
`T_(1)=T_(2)=T`
`therefore p_(1)V_(1)+p_(2)V_(2)=pV`
`therefore (p_(0)+(4S)/(r_(1)))((4)/(3)pir_(1)^(3))+(p_(0)+(4S)/(r_(2)))((4)/(3)pir_(2)^(3))=(p_(0)+(4S)/(r ))((4)/(3)pir^(3))`
Solving, this we get
`S=(p_(0)(r^(3)-r_(1)^(3)-r_(2)^(3)))/(4(r_(1)r^(2)+r_(2)^(2)-r^(2)))`