Eight equal drops of water are falling through air with a steady velocity of 10 cm`s^(-1)`.If the drops combine to form a single drop big in size,then the terminal velocity of this big drop is

Options

A. 40 cm `s^(-1)`
B. 10 cm `s^(-1)`
C. `30cm s^(-1)`
D. `80cms^(-1)`

Answer

A

Explanation

Terminal velocity v`=(2r^(2))/(9eta)(p-sigma)g`
`rArrvpropr^(2)`
When 8 drops combine to form a single drop then
`rArrR=2r`
`therefore(v_(2))/(v_(1))=(R^(2))/(r^(2))`
`(v_(2))/(v_(1))=(4R^(2))/(r^(2))=4`
`v_(2)=4v_(1)rArrv_(1)=4xx10=40` cm/s
So correct choice is (a).