The velocity of a small ball of mass and density , when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is , then the viscous force acting on the ball will be [2021]

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Solution

Q.
The velocity of a small ball of mass $M$ and density $d$ , when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{d}{2}$ , then the viscous force acting on the ball will be [2021]

1 $2 M g$

2 $\frac{M g}{2}$

3 $M g$

4 $\frac{3}{2} M g$

Ans.
(2)

Given, Mass of ball = M

Density of ball = $d$

Density of given wire = $\frac{d}{2}$

Viscous force = weight - buoyant force

$= v d g - v (\frac{d}{2}) g$

$= v d g (1 - \frac{1}{2}) = \frac{v d g}{2}$ ...(i)

Also mass, $M = v d$

So, from equation (i),

$Viscous force = \frac{M g}{2}$

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