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  4. A tiny ball of mass 100 g and density 2 g / cm 3 is dropped in a tall jar of oil of density 0.8 g / cm 3. When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is.

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Q. A tiny ball of mass $100\, g$ and density $2\, g / cm ^{3}$ is dropped in a tall jar of oil of density $0.8\, g / cm ^{3}$. When the ball acquires terminal velocity, the magnitude of the viscous force acting on it in dyne is________.

Mechanical Properties of Fluids

Solution:

When the ball falls with constant velocity, then viscous force is equal to effective weight of the ball.
Volume of the ball $=V=\frac{m}{\rho_{\text {ball }}}=\frac{100}{2}=50\, cm ^{3}$
Mass of the liquid displaced by the ball
$= m'= V \rho_{ Liq }=50 \times 0.8=40\, g$
$\therefore $ Viscous force $F = mg - m' g$
$=(50-40) 980$
$=9800\, dyne$