Question

The velocity of a small ball of mass $M$ and density $\rho$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $\frac{\rho }{2},$ then the viscous force acting on the ball will be

• A. $2Mg$
• B. $\frac{Mg}{2}$
• C. $Mg$
• D. $\frac{3}{2}Mg$

Answer 1

The correct option is B $\frac{Mg}{2}$

Let $F_V$ be the viscous force and $F_B$ be the buoyant force acting on the ball.


Then, when body moves with constant velocity,

$Mg=F_B+F_V$ $[a=0]$

$\Rightarrow F_V=Mg-F_B$

$\Rightarrow F_V=\rho Vg-\frac{\rho }{2}Vg$

Where, $V$ is the volume of the ball.

$\Rightarrow F_V=\frac{\rho }{2}Vg=\frac{M}{2}g$

Hence, $\left(B\right)$ is the correct answer.