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Mechanical Properties of Fluids
Physics · Class 11NCERT pp. 180–1972 sets × 25 questions
Key facts and formulas for Mechanical Properties of Fluids, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Pressure at depth | P = Pₐ + ρ g h; gauge pressure = ρ g h |
| Pascal's law and hydraulic lift | F₁/A₁ = F₂/A₂; A₁L₁ = A₂L₂ (force gained, distance lost) |
| Continuity | A₁v₁ = A₂v₂; narrow part means higher speed |
| Bernoulli and efflux | P + ½ρv² + ρgh = constant; v = √(2gh) |
| Buoyancy and floating | F_b = ρ V g; floating: ρ_body V = ρ_liquid V_sub |
| Stokes terminal speed | v_t = 2a²(ρ − σ)g / 9η; v_t ∝ a² |
| Surface tension | S = F/2l for a film; surface energy = S × area |
| Excess pressure | Drop 2S/r; soap bubble 4S/r; film edge 2S/d |
| Capillary rise | h = 2S cosθ / (ρ g a); effective g changes h |
| Viscosity and flow | η: Pa s, falls for liquids and rises for gases with heat; Q ∝ r⁴ |
Three sample questions
Q1. A fluid differs from a solid mainly because a fluid
- cannot be compressed at all
- yields continuously even to a very small shearing force
- has no weight
- has no density
Hint and solution
Hint: Think about what happens when you push a fluid sideways. Does it hold a shape the way a solid does?
- Fluid: continuous yield under shear — A solid resists a sideways (shear) push and keeps its shape. We compare this with a fluid.
- Fluid shear resistance is almost zero — A fluid cannot hold a shear. It yields and flows continuously, taking the shape of its container.
- Weight, density, compressibility are shared — Fluids have weight and density, and they can be compressed a little or a lot. So those options do not give the difference.
- Answer: B — So a fluid differs because it yields continuously even to a very small shearing force. Option B.
Answer: B. A fluid cannot resist shear, so it flows and takes the shape of its vessel.
Q2. The dimensions of pressure are the same as those of
- energy per unit area
- force per unit volume
- momentum
- energy per unit volume
Hint and solution
Hint: Write pressure as force per area and reduce to M, L, T. Then check which option gives the same powers.
- P = F / A — Pressure is force divided by area. Force has dimensions M L T⁻².
- [P] = [M L T⁻²] / [L²] = [M L⁻¹ T⁻²] — Dividing by L² lowers the length power from 1 to −1.
- Energy / volume = [M L² T⁻²] / [L³] — This simplifies to [M L⁻¹ T⁻²], the same as pressure. The other options give different powers.
- Answer: D — Pressure has the same dimensions as energy per unit volume. Option D.
Answer: D. Pressure = [M L⁻¹ T⁻²], and energy / volume = [M L² T⁻²] / [L³] = [M L⁻¹ T⁻²].
Q3. Which statements about pressure in a fluid at rest are correct? (i) Pressure is a scalar. (ii) At a point it is the same in all directions. (iii) It is the same at all points on a horizontal plane in a connected liquid. (iv) The force on a surface is parallel to the surface.
- (i), (ii) and (iii) only
- (i) and (iv) only
- (ii), (iii) and (iv) only
- (iii) and (iv) only
Hint and solution
Hint: Which direction does a fluid at rest push on a wall? Think about whether it can ever push sideways along the surface.
- Static fluid: force ⟂ surface — A fluid at rest cannot hold shear, so it pushes only along the normal to a surface. Statement (iv) is false.
- Pressure is a scalar, same in all directions — At a point the pressure has no direction. So (i) and (ii) are true.
- P = Pₐ + ρ g h depends on depth only — On one horizontal plane the depth is the same, so the pressure is the same. (iii) is true.
- Answer: (i), (ii), (iii) — The correct statements are (i), (ii) and (iii) only. Option A.
Answer: A. The force of a static fluid on a surface is normal to it, so (iv) is false.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.