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These are complete exercise solutions for Samacheer Kalvi 9th Science Chapter 3 — Fluids. Solve each question yourself first, then verify below. Always show formula, substitution, and units in numerical problems. If you get stuck on a concept, revisit the Key Concepts table before retrying the question.
Key Concepts (Quick Recap)
| Term | Definition |
|---|
| Pressure | Force acting perpendicularly on a unit area; P = F/A; SI unit is pascal (Pa = N/m²) |
| Thrust | Total force acting perpendicular to a surface; SI unit is newton (N) |
| Pascal's law | Pressure applied at any point in a confined fluid is transmitted equally and undiminished in all directions |
| Liquid pressure | Pressure at a depth h in a liquid: P = ρgh; increases with depth and density |
| Buoyant force (upthrust) | Upward force exerted by a fluid on an immersed body, equal to the weight of fluid displaced |
| Archimedes' principle | When a body is partially or wholly immersed in a fluid, upthrust = weight of fluid displaced |
| Density | Mass per unit volume; ρ = m/V; SI unit kg/m³ |
| Relative density | Ratio of density of a substance to density of water; no units (it is a dimensionless ratio) |
| Floatation condition | Body floats if density < fluid density; sinks if density > fluid density; suspends if equal |
| Atmospheric pressure | Pressure exerted by the weight of the air column above a surface; ≈ 1.013 × 10⁵ Pa at sea level |
| Hydraulic press | Device using Pascal's law to multiply force; F₂ = F₁ × (A₂/A₁) |
| Hydrometer | Instrument measuring liquid density; works on Archimedes' principle / law of floatation |
I. Choose the Best Answer
Q1. The weight of the body immersed in a fluid appears to be less due to: (a) viscosity (b) upthrust ✓ (c) surface tension (d) atmospheric pressure
Answer(b) ✓ — The fluid exerts an upward force (upthrust) reducing the apparent weight.
Q2. Two bodies of different masses are dropped from the same height in vacuum. They: (a) reach the ground at different times (b) reach the ground at the same time ✓ (c) the heavier one reaches first (d) the lighter one reaches first
Answer(b) ✓ — In vacuum, there is no air resistance; all objects fall with the same acceleration g.
Q3. The upthrust depends on: (a) volume of the liquid (b) mass of the liquid (c) volume of the immersed body ✓ (d) mass of the immersed body
Answer(c) ✓ — Upthrust = ρ × V × g, where V is the volume of the immersed part of the body.
Q4. A body floats when: (a) density of body > density of liquid (b) density of body < density of liquid ✓ (c) density of body = density of liquid (d) none of these
Answer(b) ✓ — A body floats when its density is less than that of the liquid. If equal, it stays suspended; if more, it sinks.
Q5. The SI unit of pressure is: (a) newton (b) joule (c) pascal ✓ (d) kg/m³
Answer(c) ✓ — The pascal (Pa) is defined as one newton per square metre (N/m²).
Q6. A hydraulic press works on the principle of: (a) Archimedes' principle (b) Pascal's law ✓ (c) Newton's third law (d) Law of floatation
Answer(b) ✓ — A hydraulic press uses Pascal's law: pressure applied to a confined fluid is transmitted equally throughout, enabling force multiplication.
Q7. The instrument used to measure the density of a liquid is: (a) barometer (b) manometer (c) hydrometer ✓ (d) lactometer
Answer(c) ✓ — A hydrometer measures liquid density based on how deep it sinks (Archimedes' principle). A lactometer is a specialised hydrometer for milk.
Q8. Atmospheric pressure at sea level is approximately: (a) 10⁵ Pa ✓ (b) 10³ Pa (c) 10⁷ Pa (d) 10 Pa
Answer(a) ✓ — Standard atmospheric pressure is about 1.013 × 10⁵ Pa ≈ 10⁵ Pa at sea level.
Q9. As we go higher above sea level, atmospheric pressure: (a) increases (b) decreases ✓ (c) remains the same (d) first increases then decreases
Answer(b) ✓ — The column of air above decreases with altitude, so atmospheric pressure decreases as we go higher.
II. Fill in the Blanks
1. The force acting on a unit area of a surface is called pressure. 2. The upthrust experienced by a body in a fluid is equal to the weight of the fluid displaced. 3. The hydrometer works on the principle of Archimedes' principle (law of floatation). 4. Pressure at a point inside a liquid is directly proportional to the depth of the point from the surface. 5. The atmospheric pressure at sea level is approximately 1.013 × 10⁵ Pa (101325 Pa). 6. The ratio of the density of a substance to the density of water is called relative density. 7. In a hydraulic press, if the area of the larger piston is 10 times the area of the smaller piston, the force is multiplied 10 times. 8. A body floats when the weight of the body is equal to the weight of the fluid displaced by it. 9. The pressure exerted by a liquid column of height h and density ρ is given by the formula P = ρgh.
III. True or False
1. The upthrust acts in the upward direction.
AnswerTrue ✓
2. Pressure at a point inside a liquid is the same in all directions at the same depth.
AnswerTrue ✓ (Pascal's law extension)
3. A body will float if its density is greater than that of the liquid.
AnswerFalse — Correction: A body floats when its density is less than that of the liquid.
4. The buoyant force depends on the shape of the body.
AnswerFalse — Correction: Buoyant force depends on the volume of fluid displaced, not the shape of the body.
5. Pascal's law holds for gases as well as liquids.
AnswerTrue ✓ — Pascal's law applies to all confined fluids (both liquids and gases).
6. Relative density has the same unit as density.
AnswerFalse — Correction: Relative density is a ratio of two densities, so it has no units. Density has the unit kg/m³.
7. The pressure at the bottom of a dam is less than the pressure at the top.
AnswerFalse — Correction: Pressure increases with depth (P = ρgh), so the bottom of a dam experiences greater pressure than the top.
8. An object that sinks in water will always sink in salt water.
AnswerFalse — Correction: Salt water is denser than fresh water. An object that sinks in fresh water may float in salt water if its density lies between the two.
IV. Match the Following
| Column I | Column II |
|---|
| Pressure | (d) N/m² (Pascal) |
| Upthrust | (a) Weight of displaced fluid |
| Density | (c) Mass/Volume |
| Relative density | (b) Density of substance / Density of water |
| Hydraulic press | (e) Pascal's law |
| Hydrometer | (g) Archimedes' principle |
| Atmospheric pressure | (f) Weight of air column |
| Liquid pressure at depth h | (h) ρgh |
V. Answer Briefly
Q1. Define pressure.
Answer
Pressure is the force acting perpendicularly on a unit area of a surface. Mathematically, P = F/A where F is force in newtons and A is area in square metres. The SI unit of pressure is the pascal (Pa), which equals one newton per square metre (N/m²). A small force applied over a tiny area can produce a large pressure, which is why a needle can pierce skin easily.
Q2. Define upthrust (buoyant force).
Answer
Upthrust, or buoyant force, is the upward force exerted by a fluid on a body that is wholly or partially immersed in it. According to Archimedes' principle, this upward force equals the weight of the fluid displaced by the immersed part of the body. Upthrust acts vertically upward and is the reason objects feel lighter when submerged in water. The magnitude of upthrust depends on the density of the fluid and the volume of the body immersed.
Q3. Why does a ship made of iron float while an iron nail sinks?
Answer
A ship is shaped with a hollow structure that displaces a large volume of water, so the weight of the displaced water (upthrust) equals the total weight of the ship, allowing it to float. In contrast, an iron nail is solid and displaces very little water, so the upthrust is much smaller than the nail's weight, causing it to sink. The key difference lies in the overall density: the ship's average density (including the hollow air-filled space) is less than water, while the nail's density is greater than water.
Q4. State Pascal's law.
Answer
Pascal's law states that the pressure applied at any point in a confined fluid is transmitted equally and undiminished in all directions throughout the fluid. This means if you apply pressure at one point in a closed container filled with fluid, the same pressure appears at every other point in the fluid. This principle is the working basis of hydraulic machines such as hydraulic presses, hydraulic brakes, and hydraulic lifts.
Q5. Why are dams built broader at the bottom?
Answer
Liquid pressure increases with depth according to the formula P = ρgh. Near the bottom of a dam, the water depth is greatest, so the pressure exerted by the water on the dam wall is at its maximum. To withstand this large pressure, the dam walls are designed to be thicker and broader at the base. At the top, where the water depth and hence pressure are lower, the wall can be narrower. This tapered shape ensures structural stability while optimising material usage.
Q6. Differentiate between thrust and pressure.
Answer
| Thrust | Pressure |
|---|
| Total force acting perpendicular to a surface | Force per unit area |
| Unit: newton (N) | Unit: pascal (Pa = N/m²) |
| Depends on total force applied | Depends on force and area of contact |
| Example: a 50 N push on a wall | Example: the same 50 N push spread over 0.5 m² gives 100 Pa |
Q7. Explain why a person weighs less in water than in air.
Answer
When a person stands in water, the water exerts an upthrust equal to the weight of the water displaced by the person's body. This upthrust acts upward, partially counterbalancing the person's true weight. As a result, the apparent weight (what a scale would read) is less: Apparent weight = True weight − Upthrust. In air, the upthrust from air is negligible compared to that from water, so the person's apparent weight is nearly equal to the true weight.
Q8. What is relative density? Why does it have no unit?
Answer
Relative density is the ratio of the density of a substance to the density of a reference substance (usually water at 4 °C). Mathematically, Relative density = ρ_substance / ρ_water. Since it is a ratio of two quantities with the same unit (kg/m³), the units cancel out, making relative density a dimensionless quantity with no unit. A relative density greater than 1 means the substance is denser than water and will sink; less than 1 means it will float.
VI. Answer in Detail
Q1. Describe an experiment to demonstrate that pressure increases with depth in a liquid.
Answer
Aim: To show that liquid pressure increases with depth.
Materials required: A tall cylindrical container (or a plastic bottle) with three holes at different heights (top, middle, bottom), water.
Procedure: 1. Take a tall cylindrical container and make three small holes at different heights — one near the top, one in the middle, and one near the bottom. 2. Fill the container completely with water and observe the water jets emerging from each hole.
Observation:
- Water from the bottom hole travels the farthest horizontally and with the greatest speed.
- Water from the middle hole travels a moderate distance.
- Water from the top hole travels the shortest distance.
ExplanationThe pressure at each hole depends on the depth of water above it (P = ρgh). The bottom hole has the greatest depth of water above it, producing the highest pressure and the strongest jet. The top hole has the least depth above it, so the pressure and jet speed are lowest.
Conclusion: Liquid pressure increases with depth. This is why the walls of dams are built thicker at the base and why deep-sea divers experience enormous water pressure.
Q2. Explain the factors affecting buoyant force.
Answer
The buoyant force (upthrust) on a body immersed in a fluid is given by F_b = ρ × V × g, where ρ is the density of the fluid, V is the volume of fluid displaced, and g is the acceleration due to gravity. The factors affecting buoyant force are:
1. Volume of the immersed body (V): A larger volume displaces more fluid, resulting in greater buoyant force. A fully submerged cube experiences more upthrust than a smaller cube of the same material because it displaces a greater volume of fluid.
2. Density of the fluid (ρ): The denser the fluid, the greater the buoyant force. An egg that sinks in fresh water (ρ ≈ 1000 kg/m³) can float in salt water (ρ ≈ 1025 kg/m³) because the denser salt water provides more upthrust.
3. Acceleration due to gravity (g): Since F_b = ρVg, buoyant force is directly proportional to g. On the Moon where g is about 1/6th of Earth's, the same object in the same fluid would experience less buoyant force.
What does NOT affect buoyant force: The mass, shape, and material of the immersed body do not affect the buoyant force. Only the volume of fluid displaced matters. Two objects of different materials but the same immersed volume experience the same buoyant force in the same fluid.
Q3. Explain floating and sinking using density.
Answer
Whether an object floats or sinks in a fluid is determined by comparing the density of the object (ρ_object) with the density of the fluid (ρ_fluid):
1. Float (ρ_object < ρ_fluid): When the object's density is less than the fluid's density, the weight of the displaced fluid exceeds the weight of the object at full submersion. The object rises until the weight of fluid displaced equals its own weight, and it floats partially above the surface. Examples: wood on water, a ship on seawater.
2. Suspend (ρ_object = ρ_fluid): When densities are equal, the buoyant force exactly equals the object's weight at any depth. The object remains suspended wherever it is placed in the fluid — it neither rises nor sinks further. Example: an egg in salt water of matching density.
3. Sink (ρ_object > ρ_fluid): When the object's density is greater than the fluid's density, even full submersion produces a buoyant force less than the object's weight. The object sinks to the bottom. Examples: an iron nail in water, a stone in water.
Real-world application — Submarine: A submarine has ballast tanks that can be filled with water (increasing overall density to sink) or filled with compressed air (decreasing overall density to rise). By controlling the amount of water in the ballast tanks, the submarine can float on the surface, suspend at any depth, or sink as needed.
Key formula:
Fraction submerged = ρ_object / ρ_fluid
For a floating body, the fraction of volume below the surface equals the ratio of the object's density to the fluid's density.
Q4. Describe the construction and working of a hydraulic press.
Answer
Construction: A hydraulic press consists of two connected cylinders of different cross-sectional areas, both filled with an incompressible fluid (usually oil). A small piston of area A₁ fits into the narrower cylinder, and a large piston of area A₂ fits into the wider cylinder. A platform on the large piston supports the heavy load to be lifted or compressed.
Working principle — Pascal's law: According to Pascal's law, pressure applied to a confined fluid is transmitted equally and undiminished in all directions. When a small force F₁ is applied to the smaller piston:
Pressure P = F₁ / A₁
This pressure is transmitted through the fluid to the larger piston:
P = F₂ / A₂
Since pressure is the same throughout the fluid:
F₁ / A₁ = F₂ / A₂
F₂ = F₁ × (A₂ / A₁)
If A₂ is 50 times A₁, then a force of 100 N on the small piston produces 5000 N on the large piston — a mechanical advantage of 50.
Applications:
- Car lifts in service stations
- Hydraulic brakes in automobiles
- Hydraulic jacks for lifting heavy loads
- Compressing cotton bales and metal sheets in industries
Note: Although force is multiplied, there is no violation of conservation of energy. The small piston must move a much greater distance than the large piston, so work input equals work output (neglecting friction): F₁ × d₁ = F₂ × d₂.
VII. Numerical Problems
Q1. A force of 200 N acts on an area of 4 m². Calculate the pressure.
P = F / A = 200 / 4 = 50 Pa
Q2. A block of wood of volume 0.5 m³ floats in water. If 60% of the volume is submerged, find the density of wood.
Volume submerged = 0.6 × 0.5 = 0.3 m³
Weight of wood = Weight of water displaced
ρ_wood × V × g = ρ_water × V_submerged × g
ρ_wood × 0.5 = 1000 × 0.3
ρ_wood = 600 kg/m³
Q3. A hydraulic press has pistons of area 0.01 m² and 0.5 m². If a force of 100 N is applied on the smaller piston, find the force on the larger piston.
F₁ / A₁ = F₂ / A₂
F₂ = F₁ × (A₂ / A₁) = 100 × (0.5 / 0.01) = 100 × 50 = 5000 N
Q4. Calculate the pressure at a depth of 5 m in a water tank. (Density of water = 1000 kg/m³, g = 10 m/s²)
P = ρgh = 1000 × 10 × 5 = 50,000 Pa = 50 kPa
Q5. An object weighs 500 N in air and 400 N in water. Find the upthrust and volume of the object.
Upthrust = 500 − 400 = 100 N
Upthrust = ρ × V × g → 100 = 1000 × V × 10
V = 100 / 10000 = 0.01 m³
Common Mistakes to Avoid
1. ❌ Confusing pressure and force → ✅ Pressure = Force / Area. A needle pierces because area is tiny, not because force is large.
2. ❌ Writing buoyant force as ρV without g → ✅ Buoyant force = ρVg. Always include the acceleration due to gravity.
3. ❌ Treating density and relative density as the same thing → ✅ Density has units (kg/m³); relative density is a ratio with no units.
4. ❌ Stating that upthrust acts downward or sideways → ✅ Upthrust always acts vertically upward, opposing gravity.
5. ❌ Believing buoyant force depends on shape or material → ✅ It depends only on the volume of fluid displaced (ρVg).
6. ❌ Confusing a hydraulic press with a lever → ✅ A hydraulic press works on Pascal's law (equal pressure transmission), not on the lever principle.
7. ❌ Thinking atmospheric pressure increases with altitude → ✅ Atmospheric pressure decreases with altitude because the air column above gets shorter.
8. ❌ Writing P = ρhg instead of P = ρgh → ✅ The correct formula is P = ρgh — density (ρ), gravitational acceleration (g), then height/depth (h).
Exam Checklist
- [ ] Pressure formula P = F/A and units memorised
- [ ] Pascal's law statement and hydraulic press application
- [ ] Archimedes' principle statement and buoyancy calculation
- [ ] Conditions for floatation (density comparison)
- [ ] Liquid pressure formula P = ρgh and its derivation from first principles
- [ ] Numerical problems on pressure, buoyancy, and hydraulic press practised
- [ ] Applications: dams, ships, hydrometer, submarine understood
- [ ] Differences between thrust/pressure and float/sink conditions memorised
- [ ] Relative density formula and its unitless nature internalised
- [ ] Apparent weight formula: Apparent weight = True weight − Upthrust
- [ ] Direction of upthrust (always upward) and factors affecting buoyant force listed
- [ ] Experiment to show pressure increases with depth can be described with diagram
Internal Links
- [Chapter 3 Guide — Fluids](/school/tamil-nadu-state-board/class/9/science/fluids)
- [All Class 9 Science Solutions](/school/tamil-nadu-state-board/class/9/science/solutions)
- [Class 9 Science Subject Guide](/school/tamil-nadu-state-board/class/9/science)
