1. Tardigrade
  2. Question
  3. Physics
  4. A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to :-

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. A small sphere of radius 'r' falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity, is proportional to :-

Mechanical Properties of Solids

Solution:

Rate of heat produced
$\frac{ d Q }{ dt }= F _{ v } \times v _{ T }$
$\because v _{ T }=\frac{2 r ^{2}}{9 \eta}(\rho-\sigma) g \propto r ^{2} $
$=6 \pi \eta rv_{\textrm{T } } \times v _{ T }$
$\Rightarrow \frac{ d Q }{ dt } \propto rv _{ T }^{2} \propto r ^{5}$