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 ? ......... $cm/s$
JEE MAIN 2013, Diffcult
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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 $10cm/s$
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