A body of density $D_{1}$ and mass M is moving downward in glycerin of density $D_{2}$ . What is the viscous force acting on it when it is moving with terminal velocity?

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

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Mg\left ( 1-\frac{D_1}{D_2} \right )

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$M g D_{1}$

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$M g D_{2}$

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Solution

The correct option is A
$M g (1 - \frac{D_{2}}{D_{1}})$

Volume of the body, $V = \frac{M}{D_{1}}$

Mass of liquid displaced by body, $M^{'} = V D_{2} = \frac{M D_{2}}{D_{1}}$

Viscous force = effective weight of the body

= $M g - M^{'} g = M g - \frac{M D_{2}}{D_{1}} g$

= $M g (1 - \frac{D_{2}}{D_{1}})$

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