What is the reason a liquid’s terminal velocity depends on its radius when falling through a viscous medium?
Stokes’ law ( F = 6 π eta a v ) shows that viscous force is proportional to radius ( a ), while weight ( 4/3 π a³ rho g ) depends on a³ . At terminal velocity, these balance, making v propto a² .
Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Laws of Motion, Work Energy Power, Gravitation and System of Particles, Topic: Newton's laws, work-energy theorem and rotational dynamics.