CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

A small sphere of radius r falls from rest in a viscous liquid. Heat is produced due to friction between the liquid and the sphere. Choose the correct relation between rate of production of heat and the radius of the sphere, when terminal velocity is attained.


Your Answer
A
dQdtr3
Your Answer
B
dQdtr2
Correct Answer
C
dQdtr5
Your Answer
D
dQdt(r)32

Solution

The correct option is B dQdtr5
From Stokes's law,
Fv=6πηrVT
where,
η = coefficient of viscosity of liquid
VT= Terminal velocity of sphere

The rate of production of heat is equal to the power generated by viscous force.
dQdt=Power=FvVT=(6πηrVT)VT
dQdt=6πηrV2T=6πηr[29r2ηg(ρsρ)]2
where, ρs= density of sphere
ρ= density of liquid
dQdtr5
Hence, option (c) is the correct answer.

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
View More


People also searched for
View More



footer-image