Q107 / 200 · NEET 2021 · Physics

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

Solution

When velocity becomes constant then,

$F_{v} + F_{b} = M g$

$F_{v} = M g - F_{b}$

$= V ρ_{b} g - V ρ_{g} g$

$= V g [ρ - \frac{ρ}{2}]$

$= \frac{V g ρ}{2}$

$= \frac{(V ρ) g}{2} = \frac{M g}{2}$

Hence, the correct answer is option: 'C'.