A small metal sphere of radius a is falling with a velocity v through a vertical column of a viscous

English

Gujarati

Hindi

9-1.Fluid Mechanics

medium

A small metal sphere of radius $a$ is falling with a velocity $v$ through a vertical column of a viscous liquid. If the coefficient of viscosity of the liquid is $\eta $ , then the sphere encounters an opposing force of

$6\pi \eta {a^2}v$

$\frac{{6\eta v}}{{\pi a}}$

$6\pi \eta av$

$\frac{{\pi \eta v}}{{6 a^3}}$

Solution

According to Stokes’ law, the sphere encounters an opposing force $F$ (or viscous force) when it falls through a viscous liquid of viscosity $\eta $ with a velocity $v$ and it is given by

$f = 6\pi \eta av$

Note : You can also see from the options, only option $(C)$ has the dimensions of force

Standard 11

Physics

Which of the following is not the property of an ideal fluid?

easy

State stokes’ law. By using it deduce the expression for :

$(i)$ initial acceleration of smooth sphere and

$(ii)$ equation of terminal velocity of sphere falling freely through the viscous medium.

$(iii)$ Explain : Upward motion of bubbles produced in fluid.

hard

How coefficient of liquid and gas depend on temperature ?

medium

The terminal velocity $\left( v _{ t }\right)$ of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as

easy

(JEE MAIN-2022)

A steel ball is dropped in a viscous liquid. The distance of the steel ball from the top of the liquid is shown below. The terminal velocity of the ball is closest to ………. $m/s$

hard

(KVPY-2019)