A spherical soap bubble of radius 1 cm is formed inside another of radius 4 cm. The radius of single soap bubble which maintains the same pressure difference as inside the smaller and outside the larger soap bubble is_____cm.

Options

A. 0.75cm
B. 0.75cm
C. 7.5cm
D. 7.5cm

Answer

A

Explanation

Pressure outside the bigger drop `= P_(1)`
Pressure inside the bigger drop `= P_(2)`
Radius of bigger drop, `r_(1) = 3cm`
Excess pressure `= P_(2) - P_(1) = (4S)/(r_(1)) = (4S)/(3)`
Pressure inside the smaller drop `= P_(3)`
Excess pressure `= P_(3) - P_(2) = (4S)/(r_(2)) = (4S)/(1)`
Pressure difference between inner side of smaller drop and outer side of bigger drop
`=P_(3) -P_(1) = P_(3) - P_(2) + P_(2) - P_(1) = (4S)/(1) + (4S)/(3) = (16S)/(3)`
This pressure difference shoudl exist in a single drop of radius r.
`:. (4S)/(r ) = (16S)/(3) or r= (3)/(4) cm = 0.75cm`