A spherical soap bubble of radius 1 cm is formed inside another of radius 3 cm. The radius of a single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is

Options

A. 0.5cm
B. 1.0cm
C. 1.5cm
D. 2.0cm

Answer

C

Explanation

Difference of pressure inside the smaller bubble and outside the larger bubble
`Deltap = (4p)/r_(1) - (4p)/r_(2)`
'R' is the radius of single large soap bubble
`(4p)/R = (4p)/r_(1) - (4p)/r_(2)`( Given condition)
`implies 1/R = 1/r_(1) - 1/r_(2)`
`=(r_(1)r_(2))/(r_(2)-r_(1)) = 3/2 = 1.5 cm`