A small ball of mass m and density rho is dro | vedclass

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(D) When the ball falls with a constant velocity (terminal velocity),the net force acting on it is zero.The forces acting on the ball are:$1$. Weight

Vedclass · Accepted Answer

$mg\left(1-\frac{\rho_0}{\rho}\right)$

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(D) When the ball falls with a constant velocity (terminal velocity),the net force acting on it is zero.The forces acting on the ball are:$1$. Weight of the ball $(W = mg)$ acting downwards.$2$. Buoyant force $(F_B)$ acting upwards.$3$. Viscous force $(F_v)$ acting upwards.According to the condition of constant velocity,the acceleration $a = 0$.Therefore,$mg - F_B - F_v = 0$,which implies $F_v = mg - F_B$.The buoyant force $F_B$ is equal to the weight of the displaced liquid: $F_B = V \rho_0 g$,where $V$ is the volume of the ball.Since the volume $V = \frac{m}{\rho}$,we have $F_B = \frac{m}{\rho} \rho_0 g$.Substituting this into the equation for $F_v$:$F_v = mg - \frac{m}{\rho} \rho_0 g$$F_v = mg \left(1 - \frac{\rho_0}{\rho}\right)$.

$A$ small ball of mass $m$ and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After some time,the ball falls with constant velocity. The viscous force on the ball is:

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