(D) The formula for terminal velocity $v_T$ is given by Stokes' Law: $v_T = \frac{2}{9} \frac{r^2(\rho - \rho_L)g}{\eta}$.Given: $r = 0.003 \ m$,$\rho

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(D) The formula for terminal velocity $v_T$ is given by Stokes' Law: $v_T = \frac{2}{9} \frac{r^2(\rho - \rho_L)g}{\eta}$.Given: $r = 0.003 \ m$,$\rho_L = 1260 \ kg \cdot m^{-3}$,$\rho = 2 \times \rho_L = 2520 \ kg \cdot m^{-3}$,$\eta = 1.260 \ N \cdot s \cdot m^{-2}$,and $g = 10 \ m \cdot s^{-2}$.Substituting the values:$v_T = \frac{2}{9} \times \frac{(0.003)^2 \times (2520 - 1260) \times 10}{1.260}$$v_T = \frac{2}{9} \times \frac{9 \times 10^{-6} \times 1260 \times 10}{1.260}$$v_T = 2 \times 10^{-6} \times 1000 \times 10 = 0.02 \ m \cdot s^{-1}$.The distance $d$ between the $10 \ cm$ and $20 \ cm$ marks is $10 \ cm = 0.1 \ m$.Since the ball has reached terminal velocity,the time $t$ taken is:$t = \frac{d}{v_T} = \frac{0.1 \ m}{0.02 \ m \cdot s^{-1}} = 5 \ s$.

Class 11 Physics Fluid Mechanics and Surface Tension Viscosity and Stoke's Law and Terminal Velocity

Difficult

$A$ spherical ball of density $\rho$ and radius $0.003 \ m$ is dropped into a tube containing a viscous fluid filled up to the $0 \ cm$ mark as shown in the figure. The viscosity of the fluid $\eta = 1.260 \ N \cdot s \cdot m^{-2}$ and its density $\rho_L = \rho/2 = 1260 \ kg \cdot m^{-3}$. Assume the ball reaches a terminal speed by the $10 \ cm$ mark. The time taken by the ball to traverse the distance between the $10 \ cm$ and $20 \ cm$ mark is $(g = 10 \ m \cdot s^{-2})$

A
$500 \ \mu s$
B
$50 \ ms$
C
$0.5 \ s$
D
$5 \ s$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Physics Questions

Chapter

Fluid Mechanics and Surface Tension

Subtopic

Viscosity and Stoke's Law and Terminal Velocity

The terminal velocity of a metallic ball of radius $6 \ mm$ in a viscous fluid is $20 \ cm/s$. The terminal velocity of another ball of same material and having radius $3 \ mm$ in the same fluid will be . . . . . . $cm/s$.

EasyJEE MAIN 2026

View Solution

If a ball of steel (density $\rho = 7.8 \; g \cdot cm^{-3}$) attains a terminal velocity of $10 \; cm \cdot s^{-1}$ when falling in a tank of water (coefficient of viscosity $\eta_{\text{water}} = 8.5 \times 10^{-4} \; Pa \cdot s$),then its terminal velocity in glycerine (density $\rho_{\text{gly}} = 1.2 \; g \cdot cm^{-3}$,coefficient of viscosity $\eta_{\text{gly}} = 13.2 \; Pa \cdot s$) would be nearly:

MediumAIEEE 2011

View Solution

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \,cm \,s^{-1}$. If they coalesce to form one big drop, what will be the terminal speed of the bigger drop? (Neglect the buoyancy of the air)

DifficultAP EAMCET 2009

View Solution

$A$ small spherical ball of radius $0.1 \,mm$ and density $10^{4} \,kg \,m^{-3}$ falls freely under gravity through a distance $h$ before entering a tank of water. If after entering the water the velocity of the ball does not change and it continues to fall with the same constant velocity inside the water,then the value of $h$ will be $m$. (Given $g = 10 \,m \,s^{-2}$,viscosity of water $\eta = 1.0 \times 10^{-5} \,N \,s \,m^{-2}$,density of water $\rho_w = 10^3 \,kg \,m^{-3}$)

DifficultJEE MAIN 2022

View Solution

What is the rate at which a trapped bubble of $2 \,mm$ diameter rises through a solution of density $13.6 \times 10^3 \,kg/m^3$ and coefficient of viscosity $1.5 \,cP$ (in $\,m/s$)? Assume the density of air is negligible and $g = 10 \,m/s^2$.

MediumTS EAMCET 2018

View Solution

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

Similar Questions

The terminal velocity of a metallic ball of radius $6 \ mm$ in a viscous fluid is $20 \ cm/s$. The terminal velocity of another ball of same material and having radius $3 \ mm$ in the same fluid will be . . . . . . $cm/s$.

Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6 \,cm \,s^{-1}$. If they coalesce to form one big drop, what will be the terminal speed of the bigger drop? (Neglect the buoyancy of the air)

What is the rate at which a trapped bubble of $2 \,mm$ diameter rises through a solution of density $13.6 \times 10^3 \,kg/m^3$ and coefficient of viscosity $1.5 \,cP$ (in $\,m/s$)? Assume the density of air is negligible and $g = 10 \,m/s^2$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module