Physics · Mechanical Properties Of Fluids · NEET
The ball keeps falling, so gravity keeps doing positive work on it. At terminal velocity the speed is constant, so the kinetic energy does not change. That means every bit of work gravity does is not going into speed. It is being converted into heat by the viscous force (internal friction of the liquid). So heat is produced continuously even though the ball is not speeding up.
Yes. Rate of heat produced means heat produced per second, which is exactly power. Power = Force x velocity. Here the force is the viscous drag F = 6 pi eta r v and the velocity is the terminal velocity v. So Rate of heat = F x v = 6 pi eta r v^2. Watts (joule per second) is the unit.
Start from Rate = 6 pi eta r v^2. The r in front gives one power of r. Terminal velocity v is proportional to r^2, so v^2 is proportional to r^4. Multiply: r^1 x r^4 = r^5. A common mistake is to stop at the r in front (giving r^1) or to use v proportional to r^2 only once (giving r^3). You must square v because power uses v^2.
Not quite all of gravity's work. Some work by gravity is stored as work against buoyancy, but the net driving force equals the drag. The clean way: since speed is constant, net force is zero, so the drag force equals the net downward force. The power delivered by this balance equals drag x velocity, and that entire amount becomes heat. Kinetic energy stays fixed, so nothing is stored as motion.
Use v squared overall. Power = F x v, and F itself contains one v (because F = 6 pi eta r v grows with speed). So Power = (6 pi eta r v) x v = 6 pi eta r v^2. Students who write Power = 6 pi eta r v (only one v) get the wrong dependence and the wrong answer.
A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat, when the sphere attains its terminal velocity, is proportional to:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Rate of heat = power dissipated = viscous force x terminal velocity = (6 pi eta r v) x v = 6 pi eta r v^2, measured in watts.
Because rate = 6 pi eta r v^2 and terminal velocity v is proportional to r^2. So v^2 is proportional to r^4, and r x r^4 = r^5.
No. At terminal velocity the speed is constant, so kinetic energy stays fixed. The work done by gravity is fully converted into heat in the liquid.
It is power (energy per second), measured in watts. Total heat would be power multiplied by time.
The viscous drag force, which is the internal friction between the liquid layers dragged by the moving sphere. This is described by Stokes' law, F = 6 pi eta r v.
