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Stokes' Law And Terminal Velocity - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main
Quick Facts
-
Stokes' law & Terminal Velocity is considered one the most difficult concept.
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46 Questions around this concept.
Solve by difficulty
Spherical balls of radius are falling in a viscous fluid of viscosity
with a velocity
. The retarding viscous force acting on the spherical ball is:
A spherical solid ball of volume V is made of a material of density 1. It is falling through a liquid of density
2 (
2 <
1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed
. The terminal speed of the ball is
The velocity of a small ball of mass ' $\mathrm{m}^{\prime}$ and density $\mathrm{d}_1$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $\mathrm{d}_2$, then the viscous force acting on the ball will be:
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A raindrop with radius $R=0.2 \mathrm{~mm}$ falls from a cloud at a height $h=2000 \mathrm{~m}$ above the ground. Assume that the drop is spherical throughout its fall and the force of buoyance may be neglected, then the terminal speed attained by the raindrop is : [Density of water $f_w=1000 \mathrm{~kg} \mathrm{~m}^3$ and Density of air $f_a=1.2 \mathrm{kgm}^3, g=10 \mathrm{~m} / \mathrm{s}^2$ Coefficient of viscosity of air $=1.8 \times 10^{-5} \mathrm{Nsm}^{-2]}$
From amongst following curves, which one show the variation of the velocity v with time t for a small-sized spherical body (release from rest) falling vertically downwards in a long column of a viscous liquid is best represented by
If the terminal speed of a sphere of gold is 0.2 m/s in a viscous liquid
, find the terminal speed (in m/sec) of a sphere of silver
of the same size in the same liquid.
A spherical ball with radius R is descending at a velocity of v through a viscous fluid with viscosity η. Which of the following statements is correct regarding the viscous force?
Which of the diagrams in Figure correctly shows the change in kinetic energy of an iron sphere falling freely in a lake having sufficient depth to impart it a terminal velocity?
Which of the following is true about positive terminal velocity -
(i) The body attains constant velocity in a downward direction
(ii) Example - Air bubble in a liquid
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Download EBookWhich of the following is true about the terminal velocity of a spherical body in a viscous fluid -
Concepts Covered - 1
Stokes' law & Terminal Velocity
- Stokes' law-
When a body moves through a fluid then The fluid exerts a viscous force on the body to oppose its motion.
And according to Stokes' law, the magnitude of the viscous force depends on the shape and size of the body, its speed and the viscosity of the fluid.
So for the below figure
If a sphere of radius r moves with velocity v through a fluid of viscosity ,
Then using Stokes' law the viscous force (F) opposing the motion of the sphere is given by
$
F=6 \pi \eta r v
$
Where
$\eta$ - coefficient viscosity
$r$ - radius
$v-v e l o c i t y$
- Terminal Velocity-
When the spherical body is dropped in a viscous fluid, it is first accelerated and then it's acceleration becomes zero and it attains a constant velocity and this constant velocity is known as terminal velocity.
For a spherical body of radius r is dropped in a viscous fluid, The forces acting on it are shown in the below figure.
So Forces acting on the body are
1. Weight of Body (W)
$
W=m g=\frac{4}{3} \pi r^3 \rho g
$
Where $\rho \rightarrow$ density of body
2. Buoyant/ Thrust Force (T of $F_B$ )
$
T=F_B=\frac{4}{3} \pi r^3 \sigma g
$
where $\sigma \rightarrow$ density of fluid
3. Viscous force (F)
$
F=6 \pi \eta r v
$
So when the body attains terminal velocity the net force acting on the body is zero.
Apply force balance
$
\begin{aligned}
& F_B+F=W \\
& \rightarrow 6 \pi \eta r v+\frac{4}{3} \pi r^3 \sigma g=\frac{4}{3} \pi r^3 \rho g \\
& \rightarrow 6 \pi \eta r v=\frac{4}{3} \pi r^3 g(\rho-\sigma) \\
& \rightarrow v_t=\frac{2}{9} \frac{r^2(\rho-\sigma)}{\eta} g
\end{aligned}
$
Where $v_T=$ terminal velocity
From this formula, we can say that
- Terminal velocity depends on the radius of the sphere/body.
- Greater the density of solid greater will be the terminal velocity
- Greater the density and viscosity of the fluid lesser will be the terminal velocity.
- If ρ > σ then Terminal velocity will be positive.
I.e Spherical body attains constant velocity in a downward direction.
- If ρ < σ then Terminal velocity will be negative.
I.e Spherical body attains constant velocity in an upward direction.
- Terminal velocity graph
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