On which factors does terminal velocity depend? Explain.

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(N/A) Terminal velocity $(v_t)$ is the constant velocity attained by an object falling through a viscous fluid when the net force acting on it becomes zero. According to Stokes' Law,the terminal velocity of a spherical object of radius $r$ and density $\rho$ falling through a fluid of viscosity $\eta$ and density $\sigma$ is given by the formula: $v_t = \frac{2}{9} \frac{r^2 g (\rho - \sigma)}{\eta}$.
Based on this formula,terminal velocity depends on the following factors:
$1$. Radius of the object $(r)$: Terminal velocity is directly proportional to the square of the radius $(v_t \propto r^2)$. Larger objects fall faster.
$2$. Density difference $((\rho - \sigma))$: It depends on the difference between the density of the object and the density of the fluid. If the object is denser than the fluid,it falls downwards; if the fluid is denser,the object may rise.
$3$. Viscosity of the fluid $(\eta)$: Terminal velocity is inversely proportional to the coefficient of viscosity $(v_t \propto 1/\eta)$. $A$ more viscous fluid exerts a greater drag force,reducing the terminal velocity.
$4$. Acceleration due to gravity $(g)$: Terminal velocity is directly proportional to the acceleration due to gravity $(v_t \propto g)$.

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