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Class 11  »  Physics  »  Mechanical Properties of Fluids

Variation of Pressure with Depth - UNSOLVED PRACTICE SET

Class 11

Chapter: Mechanical Properties of Fluids | Topic: Variation of Pressure with Depth

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Class 11

VARIATION OF PRESSURE WITH DEPTH - UNSOLVED PRACTICE SET

Topic: Variation of Pressure with Depth

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The pressure at depth h in a liquid of density ρ is given by:

  1. ρgh
  2. ρg/h
  3. h/ρg
  4. ρh/g

Q2. The total pressure at depth h in a liquid open to the atmosphere is:

  1. ρgh
  2. P₀ + ρgh
  3. P₀ − ρgh
  4. P₀ρgh

Q3. Two points at the same horizontal level in a static fluid have:

  1. Different pressures
  2. The same pressure
  3. Pressures depending on the container shape
  4. Zero pressure

Q4. The hydrostatic paradox states that:

  1. Pressure depends on the shape of the container
  2. Pressure at the bottom is independent of the shape of the container, depending only on depth
  3. Pressure decreases with depth
  4. Liquids exert no pressure on the sides of the container

Q5. Pressure at the bottom of a tank containing three immiscible liquids depends on:

  1. Only the bottom liquid
  2. The total height and densities of all liquids
  3. The shape of the tank
  4. Only the top liquid

Q6. If the density of a liquid is doubled and the depth is halved, the pressure at that depth:

  1. Doubles
  2. Remains the same
  3. Halves
  4. Becomes four times

Short Answer Questions

Q7. Derive the expression for pressure at depth h in a liquid of density ρ.Q. Type your question here...

Q8. Explain the hydrostatic paradox with a suitable diagram. Why does the shape of the container not affect the pressure at the bottom?

Q9. Calculate the pressure at a depth of 10 m in water. (Density of water = 1000 kg/m³, g = 9.8 m/s², atmospheric pressure = 1.01 × 10⁵ Pa)

Q10. In your school swimming pool (depth 2 m), why does your ear hurt more at the bottom than at the surface? Calculate the pressure difference.

Q11. Three immiscible liquids of densities ρ₁, ρ₂, and ρ₃ are poured into a container. Derive the expression for pressure at the bottom of the container.

Q12. Why do deep-sea divers wear special suits? What would happen to a human body at great depths without protection?

Long Answer Questions

Q13. Derive the expression for pressure variation with depth in a static fluid. Explain why pressure is the same at all points at the same horizontal level. Discuss the hydrostatic paradox with diagrams of containers of different shapes but same base area and same liquid height.

Q14. A tank contains three immiscible liquids: mercury (density 13.6 g/cm³) at the bottom to a height of 5 cm, water (density 1 g/cm³) above it to a height of 20 cm, and oil (density 0.8 g/cm³) above water to a height of 15 cm.

(a) Calculate the pressure at the mercury-water interface.

(b) Calculate the pressure at the water-oil interface.

(c) Calculate the total pressure at the bottom of the tank.

(d) Calculate the total force on the bottom of the tank if its area is 0.5 m².

(e) Draw a diagram showing the pressure variation with depth.

Q15. Analyse the design of a dam:

(a) Why are dams built thicker at the bottom than at the top?

(b) Calculate the force exerted by water on a dam wall of height 50 m and width 100 m.

(c) At what depth does the maximum pressure occur?

(d) Why is the shape of the dam curved (convex towards water) in modern designs?

(e) Discuss the factors engineers consider when designing dams for rivers in India.

Application-Based Problems

Q16. A vertical tube of length 1 m is filled with mercury (density 13.6 × 10³ kg/m³).

(a) Calculate the pressure at the bottom of the tube due to mercury alone.

(b) If the tube is now inverted and placed vertically in a mercury trough with its open end below the surface, what is the height of the mercury column remaining in the tube? (Atmospheric pressure = 76 cm of Hg)

(c) Calculate the pressure at the top of the mercury column in the inverted tube.

(d) What would happen if the tube were longer than 76 cm?

(e) Explain why this experiment demonstrates the existence of atmospheric pressure.

Q17. A submarine dives to a depth of 300 m in sea water (density 1030 kg/m³).

(a) Calculate the gauge pressure at this depth.

(b) Calculate the total pressure if atmospheric pressure is 1.01 × 10⁵ Pa.

(c) If the submarine has a circular window of radius 20 cm, calculate the force on the window.

(d) The submarine now rises to 100 m. Calculate the change in pressure on the window.

(e) Discuss why submarine hulls are made of thick steel and spherical in shape.

Q18. In a school experiment, students measure how water pressure varies with depth using a tall plastic bottle with holes at different heights.

(a) Predict what will happen when water is filled in the bottle — which hole will have the fastest jet?

(b) If the bottle has holes at 5 cm, 10 cm, and 20 cm from the top, calculate the ratio of the velocities of water emerging from each hole.

(c) Explain why the water jet from the bottom hole travels the farthest horizontally.

(d) Design an experiment to verify that pressure is proportional to depth.

(e) What would you observe if the bottle were filled with honey instead of water?


Total: 30 Marks | Time: 40 mins

Explore more topics in Mechanical Properties of Fluids

Pressure and Pascals Law Atmospheric Pressure and Gauge Pressure Archimedes Principle and Buoyancy Streamline and Turbulent Flow Equation of Continuity Bernoullis Theorem and Applications Viscosity and Stokes Law Surface Tension and Surface Energy Capillarity and Contact Angle