Eight drops of a liquid of density `rho` and each of radius a are falling through air with a constant velocity `3.75cms^(-1)` . When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

Options

A. `15xx10^(-2) ms^(-1)`
B. `2.4xx10^(-2) ms^(-1)`
C. `0.75xx10^(-2) ms^(-1)`
D. `25xx10^(-2) ms^(-1)`

Answer

A

Explanation

`V_T prop r^2`
`8 xx 4/3 pi r^3 = 4/3pi R^3`
R=2r
`implies (V_(T_1))/(V_(T_2))=((r)/(2r))^2=1/4 implies V_(T_2)=4xx3.75xx10^(-2)`
`=15xx10^(-2)` m/s