In an experiment, a small steel ball falls through a Iiquid at a constant speed of 10, cm/s . If ste

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9-1.Fluid Mechanics

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In an experiment, a small steel ball falls through a Iiquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... $cm/s$

A

$5$

B

$0$

C

$10$

D

$20$

(JEE MAIN-2013)

Solution

Weight of the body

$W = mg = \frac{4}{3}\pi {r^3}\rho g$

$T = \frac{4}{3}\pi {r^3}\sigma g$

$and\,F = 6\pi \eta vr$

When the body attains terminal velocity net force acting on the body is zero $i.e.,$

$W – T – F = 0$

And terminal velocity $v = \frac{2}{9}\frac{{{r^2}\left( {\rho – \sigma } \right)}}{\eta }g$

As in case of upward motion upward force is twice its effective weight, therefore, it will move with same speed $10cm/s$

Standard 11

Physics

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