A small soap bubble of radius 4 cm is trapped inside another bubble of radius 6 cm without any contact. Let `P_(2)` be the pressure inside the inner bubble and `P_(0)`, the pressure outside the outer bubble. Radius of another bubble with pressure difference `P_(2)-P_(0)` between its inside and outside would be :

Options

A. 6 cm
B. 12 cm
C. `4.8 cm`
D. `2. 4 cm`

Answer

D

Explanation

`P _(2) = P _(0) + (4T)/( 6) + (4t)/(4) or, P _(2) -P_(0) = (4T)/(6) + (4T)/(4) " "…(i)`
Let r be the radius of bubble with pressure difference `P _(2) - P _(0)` so,
`P_(2) - P _(0) = (4T)/® " "…(ii)`
From eq (i) and (ii),
`(4T)/(r) = (4T)/(6 ) + (4T)/(4) implies 1/r = 1/6 +1/4 implies r=2 2.4 cm`