Buoyancy — Archimedes' principle, floating
Properties of Matter
14
JEE Qs
8%
Hard
60
min
Always draw a Free Body Diagram for the object, carefully identify the exact volume of fluid displaced, and distinguish between an object's total volume and its submerged volume.
🧮 Key Formulas
✅ Key Points for JEE
- 1The buoyant force (F_B) always acts vertically upwards through the centroid of the displaced fluid. Its magnitude depends only on the density of the fluid, the volume of fluid displaced (which equals the submerged volume of the object), and acceleration due to gravity.
- 2For a floating object, the buoyant force exactly balances the object's total weight (F_B = W_object). The fraction of the object submerged is directly related to the ratio of the object's density to the fluid's density.
- 3When an object is fully submerged, the buoyant force remains constant regardless of depth (assuming uniform fluid density). Its apparent weight is its actual weight minus the buoyant force.
- 4Archimedes' principle applies to all fluids (liquids and gases). Problems often involve analyzing objects partially or fully submerged in multiple immiscible liquids.
- 5When solving problems, always draw a clear Free Body Diagram (FBD) and correctly identify the volume that is submerged in the fluid to calculate F_B.
⚠️ Common Mistakes
- ✕Using the total volume of the object (V_total) instead of the *submerged volume* (V_submerged) for calculating the buoyant force, especially when the object is partially submerged.
- ✕Confusing the density of the object (ρ_object) with the density of the fluid (ρ_fluid) in calculations, particularly when determining the fraction submerged.
- ✕Incorrectly assuming the buoyant force always equals the object's weight, without distinguishing between floating (where F_B = W_object) and submerged conditions (where F_B may be less than or greater than W_object if an external force is present).
📝 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