Question

The velocity of a small ball of mass ‘m’ and density $d_1$, when dropped in a container filled with glycerin, becomes constant after some time. If the density of glycerin is $d_2$, then the viscous force acting on the ball, will be

• A. $mg$ $\bigg(1-\frac{d_1}{d_2}\bigg)$
• B. $mg$ $\bigg(1-\frac{d_2}{d_1}\bigg)$
• C. $mg$ $\bigg(\frac{d_1}{d_2}-1\bigg)$
• D. $mg$ $\bigg(\frac{d_2}{d_1}-1\bigg)$

Answer 1

Answer: (B)

$mg$ $\bigg(1-\frac{d_2}{d_1}\bigg)$

Answer 2

Viscous force acting on the ball will be equal and opposite to net of weight and buoyant force

$⇒F_0=\frac{4}{3}\pi r^3d_1g−\frac{4}{3}\pi r^3d_2g$

$\frac{4}{3}πr^3d_1g\bigg(1−\frac{d_2}{d_1}\bigg)$

=$mg$ $\bigg(1−\frac{d_2}{d_1}\bigg)$

Therefore, Option (B) is correct