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Mechanical Properties of Fluids gives JEE Main a steady question or two every year, and they are rarely hard. Bernoulli, Torricelli, terminal velocity and surface tension each come with one formula and one standard situation. The place marks go missing is surface tension, where a soap film has two surfaces and a drop has one. Settle that today. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 to 2 questions every year, which is 4 to 8 marks.
- Surface tension, excess pressure and the work done in forming a bubble are the regular ones.
- Bernoulli, efflux and terminal velocity fill the rest.
What the syllabus says
In the syllabus (Unit 7, Properties of Solids and Liquids): Pressure due to a fluid column, Pascal’s law and its applications, the effect of gravity on fluid pressure, viscosity, Stokes’ law, terminal velocity, streamline and turbulent flow, critical velocity, Bernoulli’s principle and its applications, surface energy and surface tension, angle of contact, excess pressure across a curved surface, and surface tension applied to drops, bubbles and capillary rise.
Taken out in 2024: Reynolds number.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Pressure at a depth | P = P0 + ρgh |
| Upthrust | F = Vρg |
| Equation of continuity | A1v1 = A2v2 |
| Bernoulli’s equation | P + ½ρv2 + ρgh = constant |
| Speed of efflux | v = √(2gh), h measured from the free surface |
| Stokes law and terminal velocity | F = 6πηrv, v = 2r2(ρ − σ)g/9η |
| Excess pressure | drop 2T/R, soap bubble 4T/R |
| Work done in blowing a bubble | W = 8πR2T |
| Capillary rise | h = 2T cosθ / rρg |
The work done in blowing a bubble is 8πR2T and not 4πR2T for the same reason the excess pressure is 4T/R and not 2T/R — a soap bubble has an inner surface and an outer one, and you are creating both.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. Water flows through a horizontal pipe of varying cross-section. At the point where the speed is greatest, the pressure is
- (a) greatest
- (b) least
- (c) the same as everywhere else
- (d) exactly zero
Q2. A tank of water has a small hole at a depth h below the free surface. The speed of the water leaving the hole is
- (a) √(2gH), H being the full depth of the tank
- (b) √(2gh)
- (c) √(2g(H − h))
- (d) 2gh
Q3. A small sphere falls through a viscous liquid and reaches its terminal speed. That terminal speed is proportional to
- (a) r
- (b) r²
- (c) 1/r
- (d) r³
Q4. Two soap bubbles have radii r and 2r. The ratio of the excess pressure inside them is
- (a) 1 : 2
- (b) 2 : 1
- (c) 1 : 4
- (d) 4 : 1
Q5. The work done in blowing a soap bubble of radius R, for a liquid of surface tension T, is
- (a) 4πR2T
- (b) 8πR2T
- (c) 2πR2T
- (d) 16πR2T
Q6. A body weighs 50 N in air and 40 N when fully immersed in water. Taking g = 10 m/s2, its volume is
- (a) 10−3 m3
- (b) 10−2 m3
- (c) 10−4 m3
- (d) 1 m3
Q7. A small sphere whose density is less than that of the liquid is released at the bottom of the liquid. It
- (a) falls faster and faster
- (b) rises with a steady terminal speed
- (c) stays exactly where it is
- (d) falls, but slowly
Q8. The SI unit of surface tension is
- (a) N
- (b) N/m
- (c) N/m2
- (d) N·m
Q9. Water rises to a height h in a capillary tube of radius r. In a tube of radius r/2 it would rise to
- (a) h/2
- (b) 2h
- (c) h
- (d) 4h
Q10. Streamline flow turns into turbulent flow once the fluid exceeds a certain
- (a) critical pressure
- (b) critical velocity
- (c) critical density
- (d) critical temperature
Answer key, with a hint for each
| Q1 | (b) | Bernoulli. The three terms add to a constant, so a larger speed term forces a smaller pressure term. |
| Q2 | (b) | Torricelli’s result. Only the depth below the free surface matters, not the total depth of the tank. |
| Q3 | (b) | At terminal speed the viscous drag 6πηrv balances the weight minus the upthrust, and that net downward force goes as r³. So v ∝ r³/r = r² — double the radius and the sphere falls four times as fast. |
| Q4 | (b) | Excess pressure goes as 1/R, so the smaller bubble has twice the excess pressure. |
| Q5 | (b) | Two surfaces, each of area 4πR2, each costing T per unit area. |
| Q6 | (a) | The upthrust is 10 N, so V = F/ρg = 10/(1000 × 10). |
| Q7 | (b) | The upthrust beats the weight, so it rises, and the viscous drag soon balances the difference. |
| Q8 | (b) | Surface tension is force per unit length, or equivalently energy per unit area. |
| Q9 | (b) | h ∝ 1/r, so halving the radius doubles the rise. |
| Q10 | (b) | Below that speed the layers slide smoothly over one another; above it the flow breaks up into eddies. The changeover speed depends on the pipe and on the fluid. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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