First slide

Viscous flow/Laminar flow

Question

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 d₂, the viscous force acting on ball is

Moderate

A

$M g (1 - \frac{d_{2}}{d_{1}})$
B

$\frac{M d_{1} g}{d_{2}}$
C

$\frac{M (d_{1} + d_{2})}{g}$
D

$M d_{1} d_{2}$

Solution

Since, ball gains the constant velocity.
Therefore, net force on the ball = zero.
$\Rightarrow Weight of the ball = Buoyancy force + Viscous force (F_{v})$
$\begin{array}{l} \Rightarrow M g = \frac{M}{d_{1}} \times d_{2} \times g + F_{v} \\ ∴ F_{v} = M g (1 - \frac{d_{2}}{d_{1}}) \end{array}$

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