First slide

Viscosity

Question

A uniform solid sphere of relative density 5 is released in water filled in a long vertical tube. Its terminal velocity achieved is V. If another uniform solid sphere of same material but double the radius is released in the same water then the terminal velocity achieved will be.

Moderate

A

V
B

4V
C

$\frac{V}{4}$
D

2V

Solution

Initially the terminal velocity V of sphere of radius a is
$W_{e f f} = 6 πηαV - - - - - - (1)$ ( $W_{eff} = weight - Buoyant force)$
As the radius is doubled, mass is increased to 8 times and new terminal velocity will be
$8 W_{e f f} = 6 πη 2 {αV}^{'}$ -----------(2)
from (1) and(2) V' = 4V

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