Question 166: Properties of Matter

Question

A solid sphere, of radius R acquires a terminal velocity v
1
when falling (due to gravity) through a viscous
fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these
spheres acquires a terminal velocity, v
2
, when falling through the same fluid, the ratio (v
1
/v
2
) equals :

Accepted Answer

$${4 \over 3}$$$$\pi $$R
3
= 27 $$ 	imes $$ $${4 \over 3}$$$$\pi $$r
3
$$ \Rightarrow $$ r = $${R \over 3}$$
Terminal velocity, $${V_T} = {2 \over 9}{{{r^2}} \over \eta }\left( {{\sigma _s} - {ho _l}} ight)g$$
$$ 	herefore $$ V
T
$$ \propto $$ r
2
$$ 	herefore $$ $${{{v_1}} \over {{v_2}}} = {{{R^2}} \over {{r^2}}}$$ = $${{{R^2}} \over {{{{R^2}} \over 9}}}$$ = 9

Answer

$${1 \over 9}$$

Answer

$${1 \over {27}}$$

Answer

27

Answer

9

Properties of Matter

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