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 :

Question

Question

Answer 1

Concept:

Viscous force is the resistive force acting between the layers of the fluid. It opposes the relative motion of the layers.

This force is also known as fluid friction.

Calculation:

Let F_v be the viscous force and F_B be the Bouyant force acting on the ball.

F1 Madhuri Others 03.08.2022 D1

Then, when body moves with constant velocity

Mg = F_B + F_v [a = 0]

F_v= Mg – F_B

=dVg - \(\frac{d}{2}\).Vg (where, M = dVg and V = volume of the ball )

=\(\frac{d}{2}\).Vg

Hence, F_{V =}\(\frac{M}{2}g\)