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Eight drops of water, each of radius 2mm...

Eight drops of water, each of radius `2mm` are falling through air at a terminal velocity of `8cms^-1`. If they coalesce to form a single drop, then the terminal velocity of combined drop will be

A

`32 cm s^(-1)`

B

`30 cms^(-1)`

C

`28 cm s^(-1)`

D

`24 cm s^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the radius of bigger drop is R and smaller drop is r then
`(4)/(3)piR^(3)=8xx(4)/(3)xxpir^(2)`
or R=2r`" "…(i)`
Terminal velocity , `v prop r^(2)`
`therefore (v')/(v)=(R^(2))/(r^(2))=((2r)/(r))^(2)=4 " "("Using" (i))`
or `v'=4v=4xx8=32 cm s^(-1)`
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