The diameter of an air bubble,which was initi | vedclass

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

Question

(B) As the bubble is rising steadily,the net force acting on it is zero.Since the bubble is rising,the buoyant force $(B)$ acts upwards,while the visc

Vedclass · Accepted Answer

$11$

Vedclass · Answer

(B) As the bubble is rising steadily,the net force acting on it is zero.Since the bubble is rising,the buoyant force $(B)$ acts upwards,while the viscous drag $(F)$ and the weight $(mg)$ act downwards. Given the density of air is negligible,$mg \approx 0$.Therefore,$B = F$.Using Stokes' Law for viscous drag,$F = 6 \pi \eta R v$,and the buoyant force $B = \frac{4}{3} \pi R^3 ho g$.Equating them: $\frac{4}{3} \pi R^3 ho g = 6 \pi \eta R v$.Solving for $\eta$: $\eta = \frac{2 R^2 ho g}{9 v}$.Given: $R = 1\,mm = 10^{-3}\,m$,$ho = 1750\,kg\,m^{-3}$,$g = 9.8\,m\,s^{-2}$ (or $10\,m\,s^{-2}$),$v = 0.35\,cm\,s^{-1} = 0.35 	imes 10^{-2}\,m\,s^{-1}$.Substituting values: $\eta = \frac{2 	imes (10^{-3})^2 	imes 1750 	imes 10}{9 	imes 0.35 	imes 10^{-2}} = \frac{2 	imes 10^{-6} 	imes 17500}{3.15 	imes 10^{-2}} = \frac{0.035}{0.0315} \approx 1.11\,Pa\,s$.Since $1\,Pa\,s = 10\,poise$,$\eta = 1.11 	imes 10 = 11.1\,poise$.The nearest integer is $11$.

The diameter of an air bubble,which was initially $2\,mm$,rises steadily through a solution of density $1750\,kg\,m^{-3}$ at the rate of $0.35\,cm\,s^{-1}$. The coefficient of viscosity of the solution is (in poise,nearest integer). (The density of air is negligible).

Similar Questions

Eight equal drops of water are falling through air with a steady velocity of $10 \,cm \,s^{-1}$. If the drops combine to form a single drop, then the terminal velocity of this big drop is:

Two drops of same radius are falling through air with steady velocity of $v \ cm/s$. If the two drops coalesce,what would be the terminal velocity?

When milk is shaken in a glass,it becomes still after some time. Why?

We have three beakers $A, B$,and $C$ containing glycerine,water,and kerosene respectively. They are stirred vigorously and placed on a table. The liquid which comes to rest at the earliest 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?

Vedclass Test Series

Exam Paper Generator

Online Exam Module