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. 2.4m
B. 12cm
C. 4.8cm
D. 6cm

Answer

A

Explanation

For bigger bubble,
`P_(1)-P_(0)=(4T)/(6) .......(i)`
For smaller bubble,
`P_(2)-P_(1)=(4T)/(4) ..........(ii)`
On adding equation (i) and (ii),
`P_(2)-P(0)=(4T)/(6)+(4T)/(4) ........(iii)`
Effective radius of given combination of bubble
`P_(2)-P_(0)=(4T)/(r) .....(iv)`
From equation (iii) and (iv)
`1/r=1/6+1/4 rArr r=2.4 cm`