On which factors does terminal velocity depend? Explain.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(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 $(v_t \propto g)$.

Explore More

Similar Questions

The terminal velocity of a small sphere of radius $a$ in a viscous liquid is proportional to

$A$ small rigid spherical ball of mass $M$ is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball,then the viscous force acting on the ball will be (consider $g$ as acceleration due to gravity).

$A$ metal sphere of mass $m$ and density $\sigma_{1}$ falls with terminal velocity through a container containing liquid. The density of the liquid is $\sigma_{2}$. The viscous force acting on the sphere is

$A$ person moves in sea water at terminal velocity wearing an electronic digital watch. What is the effect on the measurement of time by the waterproof watch?

$A$ spherical solid ball of volume $V$ is made up of a material of density $\rho$. It is falling through a liquid of density $\sigma$ $(\sigma < \rho)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of the terminal speed $v_{T}$,$F = -K v_{T}^2$ $(K > 0)$. Then,the terminal speed of the ball is ($g =$ acceleration due to gravity).

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo