Viscosity — Stokes' law, terminal velocity
Properties of Matter
14
JEE Qs
8%
Hard
75
min
Always draw a free-body diagram and correctly apply Newton's second law for force balance, paying close attention to the directions of gravitational, buoyant, and viscous forces, and using the correct densities for each term.
🧮 Key Formulas
✅ Key Points for JEE
- 1Viscosity represents the internal friction within a fluid, opposing the relative motion between its layers.
- 2Stokes' Law (F_Stokes = 6πηrv) is strictly applicable only for small spherical bodies moving at low speeds (laminar flow) through a homogeneous viscous fluid.
- 3Terminal velocity (v_terminal) is reached when the net force on the object becomes zero; specifically, when the sum of gravitational force and buoyant force equals the viscous drag force.
- 4The direction of the viscous force always opposes the relative motion of the object through the fluid.
- 5Viscosity of liquids generally decreases with increasing temperature, while for gases, it generally increases with increasing temperature.
⚠️ Common Mistakes
- ✕Interchanging the densities of the object (ρ_object) and the fluid (ρ_fluid) in the terminal velocity formula or in the buoyancy term.
- ✕Incorrectly applying Stokes' law to objects that are not spherical, or to situations with turbulent flow (high speeds).
- ✕Algebraic errors in setting up the force balance equation for terminal velocity, particularly with the directions of buoyancy and viscous forces relative to gravity.
📝 Practice Questions
See allQ47.Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ . and
Q27.A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity) (1) 2 Mg (2) Mg (3) 3 2 Mg (4) Mg2
Q41. A tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s, then velocity of water leaving the point (2) will be (1) 4 m/s (2) 2 m/s (3) 6 m/s (4) 8 m/s
Q30.A massless spring gets elongated by amount x1 under a tension of 5 N . Its elongation is x2 under the tension of 7 N . For the elongation of (5x1 −2x2), the tension in the spring will be, (1) 39 N (2) 15 N (3) 11 N (4) 20 N
Q32.Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1 . The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to (1) P1 −P2 (2) (P1 −P2)4 (3) (P1 −P2)2 (4) √P1 −P2
Q48.An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3 . The difference between pressure inside the bubble and atmospheric pressure is _____ N/m2 . (Take g = 10 m/s2 )
NCERT Chapters
- Class 11 Physics Ch 10: Mechanical Properties of Fluids