In air, a charged soap bubble of radius 'R' breaks into 27 small soap bubbles of equal radius 'r '. Then the ratio of mechanical force acting per unit area of big soap bubble to that of a small soap bubble is

Options

A. `1/81`
B. `3/1`
C. `1/3`
D. `9/1`

Answer

C

Explanation

If a bubble is break into 27 small soap bubbles then the volume of single bubble of radius R and the combined volume of 27 bubbles of radius r would be constant.
`27xx` volume of small bubbles = volume of larger bubble
`rArr 27(4/3pir^(3))=4/3piR^(3)`
`rArr27r^(3)=R^(3)`
`rArrr=R/3` ...(i)
Now, the pressure inside smaller soap bubble,
`P_("small")=(4T)/r=(12T)/R` ( using the relation)
and similarly `P_("large")=(4t)/R`
`therefore` Ratio of pressure of the smaller and larger soap bubble is given as,
`(P_("larger"))/(P_("smaller"))=(4T)/RxxR/(12T)=1/3`
`P_("larger") : P_("smaller")` = 1 : 3.