The excess pressure inside a spherical drop of water is four times that of another drop. Then, their respective mass ratio is

Options

A. `1:16`
B. `8:1`
C. `1:4`
D. `1:64`

Answer

D

Explanation

Excess pressure inside soap bubble `P= (2S)/(R )`
`P_(1)= (2S)/(R_(1)), P_(2)= (2S)/(R_(2))`
`therefore (2T)/(R_(1))= 4 xx (2T)/(R_(2)) rArr R_(2)= 4R_(1)`
`(m_(1))/(m_(2)) = (V_(1)rho)/(V_(2) rho)= (4//3pi R_(1)^(3) rho)/(4//3pi R_(2)^(3) rho)= (R_(1)^(3))/(64R_(1)^(3))= (1)/(64)`