A small sphere falls from rest under gravity in a viscous medium, producing heat due to friction. Find how rate of production of heat does depend upon the radius of the sphere at terminal velocity.


Correct option is


The terminal velocity attained by a small sphere of radius r and density  falling in a medium of density  and viscosity  is given by


By Stokes’ law, the viscous (frictional) force acting on the sphere at terminal velocity v is given by    


The rate of production of heat due to force F is  


Substituting the value of v2 from eq. (i), we get   




Thus, the rate of production of heat is directly proportional to the fifth power of the radius.



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