Viscosity And Stokes' Law

Question

A small steel ball falling through a tall column of glycerine eventually moves at a constant speed; what name is given to this maximum constant velocity attained by the falling ball?

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According to NCERT Class 11, Chapter 10 (Mechanical Properties of Fluids), a body falling through a viscous fluid experiences three forces: its weight acting downward, the upward buoyant force, and the upward viscous drag described by Stokes' law, $F = 6\pi\eta r v$. As speed increases the drag grows until the net force becomes zero; thereafter the body moves with constant velocity called the terminal velocity, given by $v_t = \dfrac{2r^2(\rho - \sigma)g}{9\eta}$. The option 'escape velocity' is wrong because that concerns gravitational escape from a planet, not fluid motion. The option 'critical velocity' refers to the speed at which flow changes from laminar to turbulent, a different concept. The option 'drift velocity' belongs to charge carriers in a conductor and is unrelated to a falling ball. A sanity check confirms that once acceleration ceases the velocity is steady, which is exactly the defining feature of terminal velocity, making it the only physically correct choice.

Viscosity And Stokes' Law

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