Question

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 d/2 , then the viscous force acting on the ball will be :

(1) Mg/2 

(2) Mg 

(3) 3/2 Mg

(4) 2Mg

Answer 1

Correct option is (1) Mg/2

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

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 = \(\frac{ Mg}2\)}

Answer 2

Option : (1) Mg/2 

Mass = M

Density of ball = d

Density of glycerine = d/2