The velocity of a small ball of mass M and de | vedclass

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(B) When the velocity of the ball becomes constant,it is known as the terminal velocity. At this state,the net force acting on the ball is zero.The fo

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$Mg\left(1 - \frac{d_2}{d_1}\right)$

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(B) When the velocity of the ball becomes constant,it is known as the terminal velocity. At this state,the net force acting on the ball is zero.The forces acting on the ball are:$1$. Weight of the ball $(W = Mg)$ acting downwards.$2$. Buoyant force $(F_B = V d_2 g)$ acting upwards.$3$. Viscous force $(F_v)$ acting upwards.At equilibrium: $F_v + F_B = W$$F_v = W - F_B$$F_v = Mg - V d_2 g$Since the volume of the ball $V = \frac{M}{d_1}$,we substitute this into the equation:$F_v = Mg - \left(\frac{M}{d_1}\right) d_2 g$$F_v = Mg \left(1 - \frac{d_2}{d_1}\right)$

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

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