Question

The velocity of small ball of mass $M$ and density $d_{1}=$ when dropped a container filled with glycerine becomes constant after some time. If the density glycerine is $d_{2}$, the viscous force acting on ball is

• A. $\frac{M d_{1} g}{d_{2}}$
• B. $M g\left(1-\frac{d_{2}}{d_{1}}\right)$
• C. $\frac{M\left(d_{1}+d_{2}\right)}{g}$
• D. $M d_{1} d_{2}$

Answer 1

Answer: (B)

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