Question 277: Properties of Matter

Question

A small spherical ball of radius 0.1 mm and density 104 kg m$$-$$3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of h will be ___________ m.
(Given g = 10 ms$$-$$2, viscosity of water = 1.0 $$	imes$$ 10$$-$$5 N-sm$$-$$2).

Accepted Answer

$$\sqrt {2gh} $$ = terminal speed
$$ \Rightarrow \sqrt {2gh}  = {2 \over 9}{{{r^2}g(ho  - ho ')} \over \eta }$$
$$ = {2 \over 9} 	imes {{{{10}^{ - 8}} 	imes 10 	imes 9000} \over {{{10}^{ - 5}}}}$$
$$ \Rightarrow h = {{400} \over {2g}}$$
$$ \Rightarrow h = 20$$ m

Properties of Matter

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