Q 11-09-108JEE MainJEE Main 2022 (27 Jun, Shift 1)Medium
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 $d_2$, then the viscous force acting on the ball, will be
Answer: (B) $mg\left(1 - \dfrac{d_2}{d_1}\right)$
At terminal velocity the net force is zero:
$$F_v + F_B = mg$$
The ball's volume is $V = m/d_1$, so the buoyant force is $F_B = Vd_2 g = mg\dfrac{d_2}{d_1}$.
$$F_v = mg - mg\frac{d_2}{d_1} = mg\left(1 - \frac{d_2}{d_1}\right)$$
Solution by Sreeraj P, M.Sc Physics