CBSE Class 9 Physics Hydrostatics Notes Set 09

Thrust and Pressure

Thrust is the total force acting perpendicular to a surface; its unit is the newton. Pressure is thrust per unit area, \( P = \dfrac{F}{A} \), measured in N/m² (pascal, Pa).
1. A liquid at rest exerts force perpendicular to every surface in contact with it; if it did not, the liquid would flow sideways.
2. Pressure applied to an enclosed liquid is transmitted equally in all directions (Pascal's law), which is why blowing into a closed tube of liquid raises the pressure everywhere in it.
3. A sudden fall of atmospheric pressure at a place warns of a storm.

Archimedes' Principle

When a body is immersed in a liquid, the liquid pushes it upward with a force equal to the weight of the liquid displaced.
1. For a body of volume V in a liquid of density d: buoyant force = Vdg (or Vd in gravitational units kgf when V is in m³ and d in kg/m³).
2. Apparent weight in the liquid = actual weight - buoyant force = \( V(D - d)g \) for a fully immersed body of density D.
3. Reaction to buoyancy: the body pushes the liquid down with an equal force, so a beaker of liquid on a balance reads more by Vdg when a body is held immersed in it.
4. The same principle explains why a steel needle sinks but a steel ship floats: the ship's shape displaces water whose weight equals the weight of the ship.

Density, Relative Density and Specific Gravity

1. Density = mass / volume (kg/m³). Relative density = density of the substance / density of water at 4°C; it has no unit and is numerically equal to the specific gravity.
2. For a solid heavier than water: \( \text{specific gravity} = \dfrac{w_1}{w_1 - w_2} \), where w₁ is the weight in air and w₂ the weight in water.
3. For a liquid: \( \text{specific gravity} = \dfrac{w_1 - w_3}{w_1 - w_2} \), where w₃ is the weight of the same solid in the liquid.
4. For a light solid tied to a sinker: \( \text{specific gravity} = \dfrac{w}{w + w_0 - w_2} \), where w is the weight of the solid in air, w₀ the weight of the sinker in water and w₂ the weight of both together in water.
5. For a soluble crystal, find its specific gravity with respect to a liquid in which it does not dissolve and multiply by the specific gravity of that liquid.

Floatation

1. First law: the weight of a floating body equals the weight of the liquid displaced by its immersed part.
2. Second law: the centre of gravity of the body and the centre of buoyancy lie in the same vertical line.
3. The fraction of the volume immersed equals the ratio of the density of the body to the density of the liquid: \( \dfrac{v}{V} = \dfrac{D}{d} \).
4. For a given floating body, volume (or depth) of immersion is inversely proportional to the density of the liquid, so a ship rides higher in sea water than in river water.
5. An iceberg of density 0.92 g/cm³ floating in sea water of density 1.03 g/cm³ has \( \dfrac{0.92}{1.03} \approx 89\% \) of its volume below the surface.
6. When floating ice melts, the water level does not change, because the water formed has the same volume as the water the ice had displaced.

Hydrometers

A hydrometer is a floating instrument with a weighted bulb and a narrow graduated stem. It sinks to different depths in liquids of different density, and the mark at the liquid surface gives the specific gravity directly. Special forms are the lactometer (purity of milk), the urinometer and the acid hydrometer.

Worked Example

Example. A body of volume 0.5 m³ and overall density 800 kg/m³ is dropped in water. Does it sink? What force submerges it fully?
Weight = 0.5 x 800 = 400 kgf; the buoyant force on its full volume = 0.5 x 1000 = 500 kgf, which is more than the weight, so it floats. The extra downward force needed is 500 - 400 = 100 kgf.