Class 11

Physics

Mechanics

Mechanical Properties of Fluids

Eight drops of water, each of radius 2 mm 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:

- $32cms_{−1}$
- $30cms_{−1}$
- $28cms_{−1}$
- $24cms_{−1}$

Let the radius of bigger drop is R and smaller drop is r then

$34 πR_{3}=8×34 ×πr_{3}$

or $R=2r$ ....(i)

Terminal velocity,

$v_{t}=92 ηr_{2}(ρ−σ)g $

$v_{t}∝r_{2}$

$vv_{′} =r_{2}R_{2} =(r2r )_{2}=4$ (Using (i))

or $v_{′}=4v=4×8=32cms_{−1}$