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The velocity of small ball of mass M and density $d_1$ when dropped in a container filled with glycerin becomes constant after some time. If the density of glycerin is $d_2$ then force acting on the ball

$\begin {array} {1 1} (a)\;Mg (1-\frac{d_2}{d_1}) \\ (b)\; Mg(1+\frac{d_2}{d_1}) \\ (c)\;2Mg (1-\frac{d_2}{d_1}) \\ (d)\;none\;of\;these \end {array}$

Since the ball attains equilibrium when the velocity becomes constant.
The effective force of the liquid must balance the viscous force
Effective force $= V (d_1 -d_2)g$
But $v=\large\frac{M}{d_1}$
$\therefore$ effective viscous force $= \large\frac{M}{d_1}$$(d_1-d_2)g$
$\qquad= Mg (1- \large\frac{d_2}{d_1})$
Hence a is the correct answer.

edited Feb 18, 2014 by meena.p

+1 vote