Fluid Mechanics – NDA Physics PYQs

NDA 2026-I

Q. 1. A floating body is in stable state. Which one of the following is correct?

(a)  The centre of gravity of the body is above its centre of buoyancy.

(b)  The centre of gravity of the body is below its centre of buoyancy.

(c)  The centre of gravity of the body coincides with its centre of buoyancy.

(d)  The centre of gravity of the body is below the metacentre.

Answer: (d) The centre of gravity of the body is below the metacentre.

Explanation: For a floating body to be in stable equilibrium, its centre of gravity (G) must be below the metacentre (M). When slightly tilted, the restoring couple acts to return the body upright. If G is above M, the tilting couple is destabilising. The position of G relative to the centre of buoyancy alone is not the stability criterion: G relative to M is. Concept Tested: Stability of floating body: centre of gravity must be below the metacentre

NDA 2025-II

Q. 2. The temperature at which “vapour pressure of the liquid in an open vessel becomes equal to the atmospheric pressure” is called

(a)  Melting point

(b)  Boiling point

(c)  Liquid point

(d)  None of the above

Answer: (b) Boiling point

Explanation: Boiling point is defined as the temperature at which the vapour pressure of a liquid equals the atmospheric (ambient) pressure. At this temperature, vapour bubbles form throughout the liquid and escape: the liquid boils. Melting point is the temperature at which solid and liquid phases are in equilibrium. Concept Tested: Boiling point: temperature where vapour pressure equals atmospheric pressure

Q. 3. Which one of the following statements about surface tension is correct?

(a)  It increases when temperature increases

(b)  It decreases when temperature increases

(c)  It will remain same with increase or decrease of temperature

(d)  It will always decrease with increase or decrease of temperature

Answer: (b) It decreases when temperature increases

Explanation: Surface tension decreases as temperature increases. Higher temperature gives molecules greater kinetic energy, reducing the net inward attractive force at the liquid surface. At the boiling point, surface tension approaches zero. This is why hot water cleans better: reduced surface tension improves wetting. Concept Tested: Surface tension vs temperature: decreases as temperature increases

Q. 4. A body sinks in water when

(a)  density of water is greater than density of body

(b)  density of water is less than density of body

(c)  density of water is equal to density of body

(d)  the body is heavy

Answer: (b) density of water is less than density of body

Explanation: A body sinks when its average density is greater than the fluid density: i.e., when the density of the body exceeds the density of water. If water density < body density, the buoyant force is less than the body’s weight and the body sinks. If water density > body density, the body floats. ‘Heavy’ alone does not determine sinking: a heavy ship floats. Concept Tested: Sinking condition: body sinks when its density > water density

NDA 2025-I

Q. 5. When a solid body is partially or completely immersed in a fluid, the fluid exerts an upward force on the body. The magnitude of the force is equal to

1.  the mass of the body

2.  the weight of the displaced fluid by the body

Which of the above is/are correct?

(a)  1 only

(b)  2 only

(c)  Both 1 and 2

(d)  Neither 1 nor 2

Answer: (b) 2 only

Explanation: Archimedes’ Principle: the buoyant force equals the weight of fluid displaced (not the mass). Weight = mass × g; these differ by a factor of g ≈ 10. Statement 1 says ‘mass of the body’: wrong (buoyancy does not depend on the object’s mass, only on the displaced fluid’s weight). Statement 2 is correct. Concept Tested: Archimedes’ Principle: buoyant force = weight of displaced fluid (not mass)

★ JOVIK Exam Insight Precise language matters: buoyancy = WEIGHT of displaced fluid (in Newtons), not MASS (in kilograms). Weight = mass × g. This exact distinction was tested in NDA 2025-I. Buoyancy does not equal the mass of the displaced fluid.

NDA 2024-II

Q. 6. Shown in the figure are two hollow cubes C₁ and C₂ of negligible mass partially filled (depicted by darkened area) with liquids of densities ρ₁ and ρ₂, respectively, floating in water (density ρᵤ). The relationship between ρ₁, ρ₂ and ρᵤ is

(a)  ρ₂ < ρᵤ < ρ₁

(b)  ρ₂ < ρ₁ < ρᵤ

(c)  ρ₁ < ρ₂ < ρᵤ

(d)  ρ₁ < ρᵤ < ρ₂

Answer: (d) ρ₁ < ρᵤ < ρ₂

Explanation: Both cubes float in water, so both have average density < ρᵤ. The cube filled with liquid of density ρ₂ is partially filled yet still floats. The cube with ρ₁ floats with more filling submerged. Since both systems float and the cubes have negligible mass, the contained liquid density and fill fraction together determine average density. For the given floating conditions in the standard figure, ρ₁ < ρᵤ < ρ₂. Concept Tested: Floating hollow cubes: relating densities of contained liquid, water, and floating condition

Q. 7. A pumpkin weighs 7·5 N. On submerging completely in water, ¾L of water gets displaced. g = 10 m/s². Correct value of density of pumpkin is:

(a)  10 kg/m³

(b)  100 kg/m³

(c)  1000 kg/m³

(d)  10000 kg/m³

Answer: (c) 1000 kg/m³

Explanation: Volume of pumpkin = ¾ L = 0.75 × 10⁻³ m³. Mass = W/g = 7.5/10 = 0.75 kg. Density = m/V = 0.75/(0.75 × 10⁻³) = 1000 kg/m³. The pumpkin has the same density as water: so it is neutrally buoyant, consistent with how pumpkins float just at the water surface. Concept Tested: Density from weight and displaced volume: ρ = m/V = (W/g)/V

Q. 8. At which temperature does liquid water show maximum density?

(a)  299 K

(b)  277 K

(c)  285 K

(d)  373 K

Answer: (b) 277 K

Explanation: Water has maximum density at 4°C = 277 K. At 277 K, density = 1000 kg/m³. Above and below 4°C, water expands and becomes less dense. At 373 K (100°C), water boils. At 299 K (26°C) and 285 K (12°C), water is less dense than at 4°C. Concept Tested: Anomalous expansion of water: maximum density at 4°C = 277 K

NDA 2023-II

Q. 9. A liquid is heated up to a certain temperature. Which one of the following situations would correspond to the boiling of the liquid?

(a)  When atmospheric pressure becomes equal to the vapour pressure.

(b)  When atmospheric pressure becomes less than vapour pressure.

(c)  When atmospheric pressure becomes higher than the vapour pressure.

(d)  When vapour pressure becomes equal to the air pressure.

Answer: (d) When vapour pressure becomes equal to the air pressure.

Explanation: Boiling occurs when the vapour pressure of the liquid equals the ambient (atmospheric/air) pressure. At this point, vapour bubbles form throughout the liquid and rise to the surface. Options (a) and (d) say essentially the same thing: atmospheric pressure = air pressure = vapour pressure. Option (d) more precisely frames this as the vapour pressure rising to equal the air pressure. Concept Tested: Boiling point: occurs when vapour pressure equals atmospheric (air) pressure

★ JOVIK Exam Insight Boiling point definition: vapour pressure = atmospheric pressure. At high altitude: atmospheric pressure is lower → boiling at lower temperature. In pressure cooker: higher pressure → higher boiling point. NDA tested this in 2023-II and 2025-II.

Q. 10. An iron nail sinks in water whereas an iron ship floats. Which of the following statements is correct in this regard?

1.  Average density of ship is greater than that of the water

2.  Average density of iron nail is greater than that of the water

3.  Average density of the ship is less than that of the water

4.  Average density of the ship is equal to that of the water

Select the correct answer using the code given below:

(a)  1 and 2

(b)  2 and 3

(c)  2 and 4

(d)  1 and 4

Answer: (b) 2 and 3

Explanation: The iron nail sinks because its average density (solid iron, ~7800 kg/m³) is greater than water (1000 kg/m³): Statement 2 is correct. The iron ship floats because its average density (steel hull + enclosed air) is less than water (~1000 kg/m³): Statement 3 is correct. Statements 1 and 4 are false. Concept Tested: Float vs sink: determined by average density relative to water

Q. 11. A block of wood (dimensions: 40 cm × 20 cm × 10 cm) is kept on a tabletop in three different positions: (a) with its side of dimensions 20 cm × 10 cm; (b) with its side of dimensions 10 cm × 40 cm; and (c) with its side of dimensions 40 cm × 20 cm. The pressure exerted by the wooden block on the tabletop in these positions is represented by Pₐ, Pᴮ and Pᶜ, respectively. The pressure follows the trend

(a)  Pₐ > Pᴮ > Pᶜ

(b)  Pₐ < Pᴮ < Pᶜ

(c)  Pₐ = Pᴮ = Pᶜ

(d)  Pₐ < Pᴮ = Pᶜ

Answer: (a) Pₐ > Pᴮ > Pᶜ

Explanation: P = Weight/Area. Areas: (a) 20×10 = 200 cm², (b) 10×40 = 400 cm², (c) 40×20 = 800 cm². Weight is constant. Pressure ∝ 1/Area. Smallest area → highest pressure. Pₐ (200 cm²) > Pᴮ (400 cm²) > Pᶜ (800 cm²). Concept Tested: Pressure from solid block: smallest face area gives highest pressure; P ∝ 1/A at constant weight

NDA 2022-II

Q. 12. An object is made of two equal parts by volume; one part has density ρ₀ and the other part has density 2ρ₀. What is the average density of the object?

(a)  3ρ₀

(b)  (3/2)ρ₀

(c)  ρ₀

(d)  (1/2)ρ₀

Answer: (b) (3/2)ρ₀

Explanation: Let each part have volume V. Total mass = ρ₀V + 2ρ₀V = 3ρ₀V. Total volume = 2V. Average density = 3ρ₀V/(2V) = 3ρ₀/2 = (3/2)ρ₀. For equal volumes, average density = arithmetic mean of densities = (ρ₀ + 2ρ₀)/2 = 3ρ₀/2. Concept Tested: Average density: equal volumes: arithmetic mean of densities

Q. 13. A pressure cooker cooks food faster by

(a)  increasing the boiling point of water

(b)  decreasing the boiling point of water

(c)  increasing the melting point of water

(d)  decreasing the melting point of water

Answer: (a) increasing the boiling point of water

Explanation: A pressure cooker seals steam inside, building pressure above atmospheric. The higher pressure requires a higher temperature for vapour pressure to equal total pressure: so water boils at above 100°C. Food cooks at this higher temperature, reducing cooking time. The melting point is unaffected. Concept Tested: Pressure cooker: seals steam, raises pressure, raises boiling point above 100°C

Q. 14. The volume of a sealed packet is 1 litre and its mass is 800 g. The packet is first put inside water with density 1 g cm⁻³ and then in another liquid B with density 1.5 g cm⁻³. Then which one of the following statements holds true?

(a)  The packet will float in both water and liquid B.

(b)  The packet will sink in both water and liquid B.

(c)  The packet will sink in water but will float in liquid B.

(d)  The packet will float in water and sink in liquid B.

Answer: (a) The packet will float in both water and liquid B.

Explanation: Density of packet = mass/volume = 800 g / 1000 cm³ = 0.8 g/cm³. Since 0.8 < 1.0 g/cm³ (density of water), the packet floats in water. Since 0.8 < 1.5 g/cm³ (density of liquid B), the packet also floats in liquid B. A body floats in any liquid whose density is greater than its own average density. Concept Tested: Floating condition: density of packet (0.8 g/cm³) < both liquids; floats in both

NDA 2022-I

Q. 15. All objects experience a buoyancy when they are immersed in a fluid. Buoyancy is

(a)  a downward force

(b)  a downward pressure

(c)  an upward force

(d)  an upward pressure

Answer: (c) an upward force

Explanation: Buoyancy is the net upward force exerted by a fluid on any immersed body. It arises because fluid pressure increases with depth: the upward force on the bottom face exceeds the downward force on the top face. The result is a net upward force. It is not a pressure and not downward. Concept Tested: Buoyancy: net upward force from pressure difference; not a pressure, not downward

Q. 16. A wooden box of mass 2 kg and dimensions (30 cm × 15 cm × 10 cm) is placed on a table with sides 30 cm and 10 cm touching the tabletop. Which one of the following is the approximate pressure exerted on the table?

(a)  111.1 N/m²

(b)  222.2 N/m²

(c)  333.3 N/m²

(d)  666.6 N/m²

Answer: (d) 666.6 N/m²

Explanation: Contact area = 30 cm × 10 cm = 0.30 m × 0.10 m = 0.03 m². Weight = mg = 2 × 10 = 20 N. Pressure = F/A = 20/0.03 ≈ 666.7 N/m². The question specifies sides 30 cm and 10 cm touching the tabletop: this is the smallest face (0.03 m²), giving the highest pressure. Concept Tested: Pressure from a solid object: P = Weight/Area; smallest face gives highest pressure

NDA 2021-II

Q. 17. Buoyancy is a/an

(a)  upward pressure

(b)  downward pressure

(c)  downward force

(d)  upward force

Answer: (d) upward force

Explanation: Buoyancy (also called upthrust) is the upward force exerted by a fluid on a body immersed in it. It is a force: measured in Newtons: not a pressure. The buoyant force results from the difference in fluid pressure between the bottom and top of the submerged body (bottom pressure > top pressure), giving a net upward force. Concept Tested: Buoyancy: an upward force (in Newtons); not a pressure (N/m²)

★ JOVIK Exam Insight A precise NDA language confusion: buoyancy is an upward FORCE (N), not an upward pressure (N/m²). NDA tested this in 2021-II and again in 2022-I with nearly identical wording. Pressure acts in all directions; buoyancy is the net upward resultant.

NDA 2021-I

Q. 18. Which one of the following regarding density of water at atmospheric pressure is correct?

(a)  Density of water at 4°C is 1000 kg/m³.

(b)  Density of water at 0°C is 1000 kg/m³.

(c)  Density of water at 0°C is 100 kg/m³.

(d)  Density of water at 4°C is 10 kg/m³.

Answer: (a) Density of water at 4°C is 1000 kg/m³.

Explanation: Water has its maximum density of 1000 kg/m³ at 4°C (277 K). Below 4°C, water expands anomalously on cooling: so at 0°C the density is slightly less than 1000 kg/m³ (about 999.8 kg/m³). This anomalous expansion is unique among common liquids and is ecologically significant for aquatic life. Concept Tested: Maximum density of water: 1000 kg/m³ at 4°C (not at 0°C)

★ JOVIK Exam Insight Maximum density of water: 1000 kg/m³ at 4°C = 277 K. At 0°C, density is slightly less. NDA has tested this in 2021-I and 2024-II. The temperature 277 K = 4°C is the standard reference.

NDA 2020-I & II

Q. 19. A liquid is kept in a glass beaker. Which one of the following statements is correct regarding the pressure exerted by the liquid column at the base of the beaker?

(a)  The pressure depends on the area of the base of the beaker

(b)  The pressure depends on the height of liquid column

(c)  The pressure does not depend on the density of the liquid

(d)  The pressure neither depends on the area of the base of the beaker nor on the height of liquid column

Answer: (b) The pressure depends on the height of liquid column

Explanation: Hydrostatic pressure at the base: P = ρgh. Pressure depends on the height of the liquid column (h) and the density (ρ). It does NOT depend on the area of the base: this is the hydrostatic paradox. A narrow and a wide vessel with the same liquid height exert the same pressure at the base. Concept Tested: Hydrostatic pressure: P = ρgh; depends on height and density, not on base area

NDA 2019-II

Q. 20. Two substances of densities ρ₁ and ρ₂ are mixed in equal volume and their relative density is 4. When they are mixed in equal masses, relative density is 3. The values of ρ₁ and ρ₂ respectively are

(a)  6, 2

(b)  3, 5

(c)  12, 4

(d)  9, 3

Answer: (a) 6, 2

Explanation: Equal volume mixing: ρ_mix = (ρ₁ + ρ₂)/2 = 4, so ρ₁ + ρ₂ = 8. Equal mass mixing: ρ_mix = 2ρ₁ρ₂/(ρ₁ + ρ₂) = 3. Substituting ρ₁ + ρ₂ = 8: 2ρ₁ρ₂/8 = 3, so ρ₁ρ₂ = 12. Solving ρ₁ + ρ₂ = 8 and ρ₁ρ₂ = 12: the two values are roots of x² − 8x + 12 = 0, giving x = 6 or x = 2. So ρ₁ = 6, ρ₂ = 2. Concept Tested: Density mixture: equal volume gives arithmetic mean; equal mass gives harmonic mean

NDA 2018-I

Q. 21. Whether an object will float or sink in a liquid, depends on

(a)  mass of the object only

(b)  mass of the object and density of liquid only

(c)  difference in the densities of the object and liquid

(d)  mass and shape of the object only

Answer: (c) difference in the densities of the object and liquid

Explanation: Whether a body floats or sinks depends on the comparison of its average density with the fluid density. If average density of body > density of liquid → sinks. If average density of body < density of liquid → floats. Mass alone is insufficient (a large bubble has mass but floats). Shape matters only insofar as it determines average density. Concept Tested: Floating/sinking condition: depends on relative densities (average density of body vs liquid)

★ JOVIK Exam Insight The float/sink criterion is average density vs liquid density: not mass alone. A ship floats because its hollow hull reduces its average density below water’s. A steel nail sinks because its average density exceeds water’s. NDA tested this in 2018-I and 2025-II.

Q. 22. Which of the following statements about a fluid at rest in a cup is/are correct?

1.  Pressure is same at all the points in the fluid.

2.  Pressure is exerted on the walls.

3.  Pressure exists everywhere in the fluid.

Select the correct answer using the code given below:

(a)  1 and 2 only

(b)  2 and 3 only

(c)  1 only

(d)  1, 2 and 3

Answer: (b) 2 and 3 only

Explanation: Statement 1 is false: pressure in a fluid at rest increases with depth (P = P₀ + ρgh): it is not the same at all points. Statement 2 is correct: fluid at rest exerts pressure on all surfaces in contact with it, including the walls. Statement 3 is correct: pressure exists throughout the volume of the fluid. Concept Tested: Fluid pressure at rest: not uniform with depth; acts on walls; exists everywhere in fluid

Q. 23. Which one of the following devices is used to measure atmospheric pressure?

(a)  Ammeter

(b)  Barometer

(c)  Potentiometer

(d)  Lactometer

Answer: (b) Barometer

Explanation: A barometer measures atmospheric pressure. An ammeter measures electric current. A potentiometer measures voltage (potential difference). A lactometer measures the density (and thus purity) of milk. Aneroid barometers and mercury barometers are both used for this purpose. Concept Tested: Barometer: instrument for measuring atmospheric pressure

NDA 2017-II

Q. 24. Water boils at a lower temperature at high altitudes, because?

(a)  the air pressure is less

(b)  outside temperature is less

(c)  latent heat is less

(d)  None of the above

Answer: (a) the air pressure is less

Explanation: Boiling occurs when vapour pressure equals atmospheric pressure. At high altitudes, atmospheric pressure is lower than at sea level. The liquid reaches the required vapour pressure at a lower temperature: so it boils at a lower temperature. Outside temperature and latent heat are not the cause. Concept Tested: Boiling point at altitude: lower atmospheric pressure reduces boiling point

Q. 25. If some object is weighed when submerged in water, what will happen to its weight compared to its weight in air?

(a)  Increase

(b)  Decrease

(c)  Remain exactly the same

(d)  Increase or decrease cannot be predicted

Answer: (b) Decrease

Explanation: When an object is submerged in water, the water exerts an upward buoyant force equal to the weight of displaced water. The apparent weight = true weight − buoyant force. Since the buoyant force is always positive (upward), the apparent weight is always less than the true weight in air for any object denser than water. Concept Tested: Apparent weight: decreases when submerged due to upward buoyant force

NDA 2016-II

Q. 26. Pressure is a scalar quantity because

(a)  it is the ratio of force to area and both force and area are vectors

(b)  it is the ratio of magnitude of force to area

(c)  it is the ratio of component of force (normal to area) to area

(d)  none of the above

Answer: (c) it is the ratio of component of force (normal to area) to area

Explanation: Pressure P = F_⊥/A: the normal (perpendicular) component of force divided by area. Taking the normal component of a vector gives a scalar magnitude, and dividing by area (a scalar) keeps the result scalar. Option (a) is wrong: the ratio of two vectors can produce a scalar only under specific conditions. Option (c) correctly identifies why pressure is scalar. Concept Tested: Pressure as a scalar: defined as normal force component ÷ area

Q. 27. Along a streamline flow of fluid

(a)  the velocity of all fluid particles at a given instant is constant

(b)  the speed of a fluid particle remains constant

(c)  the velocity of all fluid particles crossing a given position is constant

(d)  the velocity of a fluid particle remains constant

Answer: (c) the velocity of all fluid particles crossing a given position is constant

Explanation: In streamline (steady) flow, the velocity at any fixed point in the fluid does not change with time: any particle passing through that point has the same velocity. Option (a) is wrong: velocity varies at different points. Option (b) is wrong: a particle can change speed as it moves through regions of different pressure. Option (d) is wrong: a particle changes velocity as it moves along the streamline. Concept Tested: Streamline flow: velocity at each fixed position is constant; all particles through a point have same velocity

NDA 2016-I

Q. 28. Matter around us can exist in three different states, namely, solid, liquid and gas. The correct order of their compressibility is

(a)  Liquid < Gas < Solid

(b)  Solid < Liquid < Gas

(c)  Gas < Liquid < Solid

(d)  Solid < Gas < Liquid

Answer: (b) Solid < Liquid < Gas

Explanation: Gases are most compressible: molecules are far apart with large empty spaces between them. Liquids are nearly incompressible: molecules are close but can move. Solids are least compressible: molecules are tightly packed in a fixed lattice, resisting compression. The correct order of increasing compressibility is: solid < liquid < gas. Concept Tested: Compressibility of matter: solid < liquid < gas (gases are most compressible)

NDA 2015-II

Q. 29. Which one of the following statements is not correct?

(a)  In steady flow of a liquid, the velocity of liquid particles reaching at a particular point is the same at all points

(b)  Steady flow is also called streamlined flow

(c)  In steady flow, each particle may not follow the same path as taken by a previous particle passing through that point

(d)  Two streamlines cannot intersect each other

Answer: (c) In steady flow, each particle may not follow the same path as taken by a previous particle passing through that point

Explanation: In steady (streamline) flow, every particle passing through a given point follows exactly the same path: this is the definition. Option (c) says particles ‘may not follow the same path’: this is false. Option (a) should read ‘the same velocity at that particular point’: option (d) is correct (streamlines never intersect). Option (c) is the false statement. Concept Tested: Streamline flow: every particle through a given point follows the same path as previous particles

★ JOVIK Exam Insight A careful wording confusion in NDA 2015-II. Steady flow means: (1) velocity at each point is constant in time, (2) particles follow identical paths (streamlines), (3) streamlines never intersect. Option (c) directly contradicts property (2): it is the incorrect statement.

NDA 2015-I

Q. 30. Which one of the following is not a result of surface tension?

(a)  Nearly spherical drop of rain

(b)  Capillary rise

(c)  Removal of dirt by soap or detergent

(d)  Flow of a liquid

Answer: (d) Flow of a liquid

Explanation: Surface tension causes: the spherical shape of raindrops (minimum surface area); capillary rise in narrow tubes; and the cleaning action of soap (which reduces surface tension, allowing water to spread and remove oily dirt). The flow of a liquid under gravity is caused by gravitational force and viscosity: not surface tension. Concept Tested: Surface tension phenomena: not responsible for flow of liquid (gravity and viscosity cause flow)

Q. 31. A person stands on his two feet over a surface and experiences a pressure P. Now the person stands on only one foot. He would experience a pressure of magnitude

(a)  4P

(b)  P

(c)  ½P

(d)  2P

Answer: (d) 2P

Explanation: Pressure = Force/Area = Weight/Area. When standing on two feet: contact area = 2A, pressure = Weight/(2A) = P. On one foot: area = A, pressure = Weight/A = 2P. Weight is constant: only the contact area changes. Halving the area doubles the pressure. Concept Tested: Pressure: P = F/A; halving contact area doubles pressure

Q. 32. A deep sea diver may hurt his ear drum during diving because of

(a)  lack of oxygen

(b)  high atmospheric pressure

(c)  high water pressure

(d)  All of the above

Answer: (c) high water pressure

Explanation: As a diver descends, water pressure increases with depth: P = P₀ + ρgh. This high external water pressure acts on the thin eardrum membrane. The air pressure inside the middle ear remains near atmospheric: so the pressure differential across the eardrum increases, risking eardrum rupture. Atmospheric pressure does not increase with depth; only water pressure does. Concept Tested: Hydrostatic pressure at depth: high water pressure can rupture eardrum

NDA 2014-I

Q. 33. Bernoulli’s principle is based on which one among the following laws?

(a)  Conservation of mass

(b)  Conservation of momentum

(c)  Conservation of angular momentum

(d)  Conservation of energy

Answer: (d) Conservation of energy

Explanation: Bernoulli’s principle states that for an ideal fluid in steady flow, the total mechanical energy per unit volume remains constant along a streamline: P + ½ρv² + ρgh = constant. This is a statement of conservation of energy applied to fluid flow. Conservation of mass gives the continuity equation (not Bernoulli’s). Concept Tested: Bernoulli’s principle: based on conservation of energy

Q. 34. A balloon filled up with gas would only go up in air if it is filled up with

(a)  a gas whose density is lower than air

(b)  a gas whose density is higher than air

(c)  cold air

(d)  water vapour

Answer: (a) a gas whose density is lower than air

Explanation: A balloon rises if the buoyant force (weight of air displaced) exceeds the total weight of the balloon (gas + envelope). This requires the average density of the filled balloon to be less than air. Filling with a denser gas, cold air (denser than warm air), or water vapour (heavier than dry air at atmospheric conditions) increases average density and does not provide lift. Concept Tested: Balloon buoyancy: rises only when filled with gas of lower density than air

NDA 2013-I

Q. 35. Specific gravity of silver is 11 and specific gravity of iron is 8. Which one among the following is the approximate relative density of silver with respect to iron?

(a)  1.4

(b)  0.7

(c)  3.0

(d)  2.8

Answer: (a) 1.4

Explanation: Relative density of silver with respect to iron = (density of silver)/(density of iron) = 11/8 = 1.375 ≈ 1.4. Specific gravity equals density relative to water. So density of silver = 11 × ρ_water and density of iron = 8 × ρ_water. Their ratio = 11/8. Concept Tested: Relative density: ratio of specific gravities; 11/8 ≈ 1.4

NDA 2012-I

Q. 36. When a solid object is immersed in water, there is a loss in its weight. This loss is

(a)  equal to the weight of the water displaced

(b)  less than the weight of the water displaced

(c)  greater than the weight of the water displaced

(d)  not related to the weight of the water displaced

Answer: (a) equal to the weight of the water displaced

Explanation: This is Archimedes’ Principle: the apparent weight loss of an object immersed in a fluid equals exactly the weight of fluid displaced. Apparent weight = true weight − buoyant force = true weight − weight of displaced water. The loss is not greater, not less: it is exactly equal. Concept Tested: Archimedes’ Principle: apparent weight loss = weight of displaced fluid

★ JOVIK Exam Insight Archimedes’ Principle appears in multiple NDA papers. The loss in weight equals the weight of fluid displaced: not the mass of fluid displaced. Weight = mass × g. This distinction between mass and weight is tested in NDA 2025-I.

Q. 37. For a steel boat floating on a lake, the weight of the water displaced by the boat is

(a)  less than the weight of the boat

(b)  more than the weight of the boat

(c)  equal to the weight of the part of the boat which is below the water level of the lake

(d)  equal to the weight of the boat

Answer: (d) equal to the weight of the boat

Explanation: A floating body displaces fluid whose weight exactly equals the weight of the floating body (Law of Flotation). For a steel boat, the hull traps air, giving the boat an average density less than water: allowing it to float. The displaced water weight equals the boat’s weight: not less, not more. Concept Tested: Law of flotation: displaced water weight = weight of floating body

NDA 2011-I

Q. 38. A liquid rises to a certain length in a capillary tube. The tube is inclined to an angle of 45°. The length of the liquid column will:

(a)  increase

(b)  decrease

(c)  remain unchanged

(d)  first decrease and then increase

Answer: (a) increase

Explanation: When a capillary tube is inclined, the vertical height of liquid rise stays the same (determined by surface tension, radius, and gravity). However, the length along the inclined tube equals h/cos θ. At 45°: L = h/cos 45° = h√2. The column length along the tube increases, while the vertical height remains unchanged. Concept Tested: Capillary rise: inclined tube: vertical height unchanged; column length increases as L = h/cos θ

Q. 39. In a pressure cooker cooking is faster because the increase in vapour pressure:

(a)  increases the specific heat

(b)  decreases the specific heat

(c)  decreases the boiling point

(d)  increases the boiling point

Answer: (d) increases the boiling point

Explanation: A pressure cooker traps steam and builds up pressure above atmospheric. Higher pressure requires a higher temperature for the vapour pressure to equal the total pressure: so the boiling point rises above 100°C. Food cooks at a higher temperature, completing faster. Specific heat is not affected. Concept Tested: Pressure cooker: higher pressure raises boiling point above 100°C; food cooks faster

★ JOVIK Exam Insight A classic NDA misconception: (1) Pressure cooker raises boiling point (not lowers it). (2) At high altitude, boiling point drops: food takes longer to cook despite water boiling sooner. Both tested in NDA. Remember: higher pressure = higher boiling point.

NDA 2010-II

Q. 40. Two identical blocks of ice, A and B, float in water as shown in the figure given above. Which one among the following statements in this regard is correct?

(a)  Block A displaces a greater volume of water since the pressure acts on a smaller bottom area

(b)  Block A displaces a greater volume of water since its submerged end is lower in the water

(c)  Block B displaces a greater volume of water since its submerged end has a greater area in water

(d)  The two blocks displace equal volumes of water since they have the same specific gravity and same mass

Answer: (d) The two blocks displace equal volumes of water since they have the same specific gravity and same mass

Explanation: Both blocks are identical: same mass and same density (specific gravity). By Archimedes’ Principle, a floating body displaces fluid equal in weight to its own weight. Since both blocks have the same weight, they displace the same weight of water, and since water has uniform density, they displace the same volume. Orientation has no effect on the volume displaced. Concept Tested: Archimedes’ Principle: floating bodies with same mass displace equal volumes regardless of orientation

Q. 41. When a ship floats on water?

(a)  it displaces no water

(b)  the mass of water displaced is equal to the mass of the ship

(c)  the mass of water displaced is lesser than the mass of the ship

(d)  the mass of water displaced is greater than the mass of the ship

Answer: (b) the mass of water displaced is equal to the mass of the ship

Explanation: A floating body displaces water equal in weight (and therefore equal in mass, since g is uniform) to its own weight/mass. This is Archimedes’ Principle for floating bodies. The ship floats because its average density (including hollow hull) is less than water, allowing it to displace enough water to support its weight. Concept Tested: Law of flotation: floating body displaces water equal in mass to its own mass

★ JOVIK Exam Insight Floating bodies: displaced mass = mass of floating body. Sinking bodies: displaced mass < mass of sinking body. A steel ship floats because its average density is less than water (hollow hull traps air). The same steel as a solid block sinks.

NDA 2010-I

Q. 42. A vessel contains oil (density ρ₁) over a liquid of density ρ₂; a homogeneous sphere of volume V floats with half of its volume immersed in the liquid and the other half in oil. The weight of the sphere is

(a)  V(ρ₂ − ρ₁)/2

(b)  V(ρ₂ + ρ₁)g/2

(c)  V(ρ₂ + ρ₁)

(d)  V(ρ₂ + ρ₁)/2

Answer: (b) V(ρ₂ + ρ₁)g/2

Explanation: The sphere floats with V/2 in the liquid (density ρ₂) and V/2 in the oil (density ρ₁). Buoyant force = weight of displaced liquid + weight of displaced oil = (V/2)ρ₂g + (V/2)ρ₁g = Vg(ρ₁ + ρ₂)/2. For floating, weight of sphere = buoyant force = V(ρ₂ + ρ₁)g/2. Concept Tested: Buoyancy in a two-fluid system: sphere floating at oil-liquid interface

---