A drop of liquid is broken down into `27` identical liquid drops. If the terminal velocity of original liquid drops is `V_(T)`, then find the terminal velocity of the new liquid drop thus formed.

Options

A. `1//27`
B. `27`
C. 9
D. `1//9`

Answer

C

Explanation

Terminal velocity for sphere of radius r
`v=2/(9 eta)(d - rho) r^(2)g`
`implies v prop r^(2)`
`r_(2)^(3)=(r_(1)^(3))/27implies(r_(1))/(r_(2))=3implies(v_(1))/(v_(2))=((r_(1))/(r_(2)))^(2)=9`