The ratio of radii of two bubbles is `2 : 1`. What is the ratio of excess pressures inside them ?

Options

A. `1 : 2`
B. `1 : 4`
C. `2 : 1`
D. `4 : 1`

Answer

A

Explanation

Excess pressure inside the bubble,
`p=(4T)/(r)`
Then, `p_(1)=(4 T)/(r_(1))" "...(i)`
`p_(2)=(4T)/(r_(2))" "...(ii)`
From Eqs. (i) and (ii), we have
`(p_(1))/(p_(2))=(4T//r_(1))/(4T//r_(2))=(r_(2))/(r_(1))`
`(p_(1))/(p_(2))=(1)/(2)`