The excess pressure inside a soap bubble of volume `V_(1)` is twice the excess pressure insie a second soap bubble of twice the excess pressure inside a second soap bubble of volume `V_(2)` .the value of the ratio `(V_(1))/(V_(2))` is

Options

A. 1
B. `1/2`
C. `1/4`
D. `1/8`

Answer

D

Explanation

Excess of pressure (P) = `(4T)/R`
` :. (4T)/R = 2 (4T)/(R_(2)) " " :. R_(2) = 2R_(1)`
and ` V_(1) = 4/3 piR_(1)^(3) and V_(2) = 4/3 piR_(2)^(3)`
` :. (V_(1))/(V_(2)) = ((R_(1))/(R_(2)))^(3) = ((R_(1))/(2R_(1)))^(3) = 1/8`