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Matter & Fluid Mechanics
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Q.1
WBCS Prelims 2006
Ethyl alcohol is completely miscible with water. It can be separated from that mixture by
A. Using a separating funnel
B. Evaporation
C. Fractional distillation
D. Allowing the water to evaporate
Explanation
Why Correct: Fractional distillation exploits the 21.2°C boiling point difference between ethanol (78.37°C) and water (100°C), allowing separation through repeated vaporization-condensation cycles.
Distractor Analysis: Separating funnels only work for immiscible liquids that form distinct layers. Simple evaporation would remove both components or leave residues. Allowing water to evaporate naturally is impractical and inefficient for complete separation.
Takeaway: For miscible liquids with different boiling points, fractional distillation is the standard laboratory method; azeotropic mixtures like ethanol-water require special techniques for complete separation.
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Q.2
WBCS Prelims 2005
The process by which the gas comes out of an L.P.G. Cylinder is called
A. Diffusion
B. Effusion
C. Pressure
D. Ventilation
Explanation
Why Correct: Effusion describes gas molecules flowing through a small opening under a pressure gradient, exactly how LPG exits a cylinder valve.
Distractor Analysis: Diffusion involves gradual mixing of gases due to random molecular motion without bulk flow. Pressure is the force per unit area exerted by gas molecules. Ventilation refers to intentional air exchange in enclosed spaces.
Takeaway: Graham's law quantifies effusion rates: lighter gases effuse faster than heavier ones at the same temperature and pressure.
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Q.3
WBCS Prelims 2001
Which of the following mixtures can be separated by using a separating funnel?
A. water + sugar
B. water + milk
C. water + oil
D. petrol + kerosene
Explanation
Why Correct: A separating funnel separates immiscible liquids based on density differences, and water and oil form two distinct layers that don't mix.
Distractor Analysis: Water and sugar form a homogeneous solution where sugar dissolves completely. Water and milk form a colloidal suspension where fat globules are dispersed but don't separate into distinct layers. Petrol and kerosene are miscible hydrocarbons that form a single homogeneous phase.
Takeaway: Separating funnels work only for immiscible liquids with different densities, not for solutions, colloids, or miscible liquids.
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Q.4
WBCS Prelims 2000
When a liquid is heated from 20°C to 60°C its density
A. Remains the same
B. Increases
C. Decreases
D. Is lost
Explanation
Why Correct: Heating increases molecular kinetic energy, causing thermal expansion that reduces mass per unit volume, so density decreases for nearly all liquids.
Distractor Analysis: Density remains constant only for incompressible fluids under specific conditions, not with temperature changes. Density increases occur with cooling, not heating, due to contraction. Density is an intensive property that cannot be 'lost' but can change numerically.
Takeaway: Water exhibits anomalous expansion with maximum density at 4°C, but for most liquids like mercury or alcohol, density decreases linearly with temperature increase.
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Q.5
WBCS Prelims 2023
For a floating body to be in stable equilibrium, where should its centre of buoyancy be located?
A. At the centre of gravity
B. Above the centre of gravity
C. Below the centre of gravity
D. It may anywhere
Explanation
Why Correct: The centre of buoyancy must lie below the centre of gravity for stable equilibrium, creating a restoring moment when the body tilts.
Distractor Analysis: At the centre of gravity produces neutral equilibrium where the body remains in any tilted position. Above the centre of gravity creates unstable equilibrium where any tilt increases. It may anywhere is factually incorrect since buoyancy position relative to gravity determines stability type.
Takeaway: For submerged bodies, stable equilibrium requires the centre of buoyancy above the centre of gravity, opposite to floating bodies.
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Q.6
WBCS Prelims 2023
A drop of water is broken into two drops. The sum of which property of the drops is equal to that of the single one?
A. Radius
B. Surface area
C. Surface energy
D. Volume
Explanation
Why Correct: Volume remains conserved during splitting because mass and density stay constant, making the total volume of the two smaller drops identical to the original drop's volume.
Distractor Analysis: Radius decreases for each smaller drop since volume scales with radius cubed. Surface area increases because multiple smaller drops have greater combined surface area than a single drop of the same total volume. Surface energy rises due to increased total surface area, which amplifies surface tension energy.
Takeaway: When a drop splits into n identical smaller drops, the radius of each smaller drop equals the original radius divided by the cube root of n, and the total surface area becomes the original area multiplied by the cube root of n.
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Q.7
WBCS Prelims 2021
A boat floating in a tank is carrying some passengers. If the passengers drink water from the tank, how will it affect the water level of the tank ?
A. It will go down.
B. It will rise.
C. It will depend on the atmospheric pressure.
D. It will remain same.
Explanation
Why Correct: Drinking water from the tank transfers mass from the tank into the passengers' bodies, but the total mass of the boat-passengers system remains unchanged, so the displaced water volume and water level stay constant.
Distractor Analysis: Water level going down would occur if mass were removed from the system entirely. Water level rising would require adding mass to the system. Atmospheric pressure affects absolute pressure but not water level changes in this closed system.
Takeaway: In floating body problems, water level depends only on the total weight of the floating system, not on internal redistribution of mass within that system.
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Q.8
WBCS Prelims 2021WBCS Prelims 2015
Hydraulic press is based on
A. Archimedes law
B. Pascal's law
C. Reynold's law
D. Bernouli's law
Asked 2 times in WBCS. High priority question.
Explanation
Why Correct: Pascal's law states that pressure applied to a confined fluid transmits equally in all directions, which is the fundamental principle behind hydraulic presses that multiply force.
Distractor Analysis: Archimedes law describes buoyancy and flotation. Reynold's law relates to fluid flow regimes and turbulence. Bernouli's law explains the relationship between pressure and velocity in fluid flow.
Takeaway: Hydraulic systems like jacks, brakes, and lifts all operate on Pascal's law, which enables force multiplication through pressure transmission in confined liquids.
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Q.9
WBCS Prelims 2020
The absorption of ink by blotting paper involves
A. viscosity of Ink
B. capillary action
C. diffusion of Ink
D. siphon action
Explanation
Why Correct: Capillary action draws ink into blotting paper through narrow pores via adhesive forces between liquid and solid and cohesive forces within the liquid.
Distractor Analysis: Viscosity measures a fluid's internal resistance to flow. Diffusion describes molecular movement from high to low concentration. Siphon action requires a tube and gravity-driven flow over a barrier.
Takeaway: Capillary rise height formula: h = (2*gamma*cos(theta))/(rho*g*r), where gamma is surface tension, theta is contact angle, rho is density, g is gravity, r is tube radius.
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Q.10
WBCS Prelims 2019
Two cars, passing each other at high speed, are in danger of side-swiping because
A. of the increase in air pressure in the space between them.
B. of decrease in the velocity of air molecules between them.
C. of decrease in air pressure in the space between them.
D. of the increase in the velocity of air molecules between them.
Explanation
Why Correct: Bernoulli's principle states that fluid pressure decreases as flow velocity increases. When two cars pass at high speed, air flows faster through the narrow gap between them, creating lower pressure that pulls the cars together.
Distractor Analysis: Increased air pressure would push the cars apart, preventing side-swiping. Decreased air velocity would increase pressure, not decrease it. Increased air velocity describes the mechanism, but the dangerous effect comes specifically from the resulting pressure decrease, not the velocity increase itself.
Takeaway: Bernoulli's principle explains lift in airplane wings, where faster airflow over the curved upper surface creates lower pressure than slower airflow underneath.
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Q.11
WBCS Prelims 2018
A body is floating in a liquid partly immersed. The body and the liquid are taken to moon. The body
A. will continue to float as before
B. floats with a greater part immersed
C. floats with lesser part immersed
D. will sink
Explanation
Why Correct: Archimedes' principle states buoyant force equals weight of displaced fluid. On the moon, both the body's weight and the liquid's weight decrease proportionally (to 1/6th Earth's value), maintaining identical weight-to-buoyancy ratio.
Distractor Analysis: Greater immersion requires increased body density relative to liquid. Lesser immersion requires decreased body density relative to liquid. Sinking requires body density exceeding liquid density, unaffected by gravity changes.
Takeaway: Flotation depends solely on relative densities—identical behavior occurs in any uniform gravitational field regardless of absolute gravity value.
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Q.12
WBCS Prelims 2017
A shaving brush is dipped in water. When taken out the hairs of the brush are seen to be drawn together due to
A. surface tension of water
B. viscosity of water
C. elasticity of hair of the brush
D. temperature difference between air and water
Explanation
Why Correct: Surface tension minimizes surface area by contracting the water film between hairs, pulling them together.
Distractor Analysis: Viscosity resists flow between layers, not contraction. Elasticity refers to material deformation under stress, not water's cohesive property. Temperature difference causes thermal expansion/contraction, not the observed cohesive effect.
Takeaway: Surface tension causes water droplets to form spheres and allows insects to walk on water.
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Q.13
WBCS Prelims 2017
The immersed portion of a piece of pure ice floating on water is
A. 8/9th of its volume
B. 9/10th of its volume
C. 10/12th of volume
D. 11/12th of volume
Explanation
Core Formula/Logic: Archimedes' principle: Weight of displaced fluid equals weight of floating object. Submerged fraction equals density ratio (object density/fluid density).
Step-by-Step Solution: 1. Density of pure ice = 0.9 g/cm3.
2. Density of pure water = 1.0 g/cm3.
3. Let total ice volume = V.
4. Let submerged volume = V_sub.
5. Weight of ice = 0.9V × g.
6. Weight of displaced water = 1.0 × V_sub × g.
7. Set equal: 0.9V = V_sub.
8. Therefore V_sub/V = 0.9 = 9/10.
Common Pitfall: Misapplying density difference as 1/9 yields 8/9 submerged (option A). Using 10/12 (5/6 ≈ 0.833) or 11/12 (≈0.917) ignores the precise 0.9 density ratio.
Shortcut/Takeaway: For ice in water, submerged fraction = 0.9/1.0 = 9/10. Memorize: ice floats with 90% submerged, 10% above water.
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Q.14
WBCS Prelims 2016
Water rises up a capillary tube because of—
A. Elasticity
B. Surface tension
C. Viscosity
D. its density
Explanation
Core Formula/Logic: Capillary action occurs due to adhesive forces between liquid and tube walls and cohesive forces within the liquid, driven by surface tension.
Step-by-Step Solution: 1. Surface tension creates a concave meniscus in narrow tubes. 2. Adhesive forces between water molecules and glass walls pull water upward. 3. Cohesive forces between water molecules maintain the column. 4. The height of rise follows Jurin's law: h = (2γ cosθ)/(ρgr), where γ is surface tension.
Common Pitfall: Confusing viscosity with surface tension leads to option C; viscosity resists flow, not causes capillary rise. Thinking density alone causes upward movement produces option D; density affects height but doesn't initiate capillary action.
Shortcut/Takeaway: Capillary rise = surface tension effect in narrow tubes; remember the formula h ∝ γ/(ρr) for quick estimation.
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Q.15
WBCS Prelims 2013
An ice cube containing a large bubble of air is floating in water contained in a large beaker. When the ice melts completely, the level of water will :
A. Remain unchanged
B. Go down
C. Rise
D. First rise and then go down
Explanation
Why Correct: The air bubble occupies volume but has negligible mass, so the ice cube displaces less water than its total volume. When the ice melts, the water from the ice plus the bubble's air volume is less than the original displaced water volume, causing the water level to fall.
Distractor Analysis: Remain unchanged applies only to pure ice floating in water without air bubbles. Rise would occur if the ice contained a denser material than water. First rise and then go down describes a thermal expansion effect not relevant here.
Takeaway: For pure ice floating in water, the water level remains unchanged upon melting because the mass of displaced water equals the mass of ice, and ice and water have the same density.
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Q.16
WBCS Prelims 2010
A tube-well will not work if the depth of water below the ground is
A. 20 ft.
B. 25 ft.
C. 28 ft.
D. 38 ft.
Explanation
Why Correct: Suction-lift tube-wells cannot operate when the water table exceeds about 30 feet because atmospheric pressure limits water lift to approximately 25-30 feet.
Distractor Analysis: 20 feet falls within the functional range of most shallow tube-wells. 25 feet approaches the maximum suction limit but remains feasible with efficient pumps. 28 feet represents the extreme upper boundary where some pumps might still operate under ideal conditions.
Takeaway: Deep tube-wells using submersible pumps can access water tables beyond 100 feet, unlike shallow suction-lift systems.
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Q.17
WBCS Prelims 2010
A piece of cotton cloth gets wet if one end of it is dipped in water in a glass. This is due to
A. Gravitation
B. Viscosity
C. Elasticity
D. Capillarity
Explanation
Why Correct: Capillary action draws water upward through narrow spaces between cotton fibers via adhesive forces between water molecules and fiber surfaces, overcoming gravity.
Distractor Analysis: Gravitation pulls objects downward, not upward. Viscosity measures a fluid's resistance to flow. Elasticity describes a material's ability to return to its original shape after deformation.
Takeaway: Capillary rise height depends inversely on tube radius (h ∝ 1/r) and directly on surface tension; it explains water movement in plants, ink in blotting paper, and wicking in fabrics.
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Q.18
WBCS Prelims 2008
Two ends of tube is closed by corks so that the tube becomes airtight. The pressure of air inside the closed tube is
A. Very small
B. Slightly less than the atmospheric pressure
C. Equal to the atmospheric pressure
D. Dependent on the length of the tube
Explanation
Why Correct: When a tube is sealed airtight at atmospheric pressure, the trapped air maintains the same pressure as the surrounding atmosphere at the moment of sealing.
Distractor Analysis: Very small pressure would only occur in a vacuum, which this setup doesn't create. Slightly less pressure would require active pumping or cooling. Pressure dependence on tube length applies only to fluid columns in vertical tubes, not sealed horizontal tubes.
Takeaway: In a sealed container at constant temperature, pressure remains constant regardless of container shape or size, following Boyle's law (P1V1 = P2V2) when volume changes.
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Q.19
WBCS Prelims 2004
When a ship enters the sea from a river, it floats up because
A. Sea water is warmer
B. the speed of the ship on the sea is greater
C. the density of the river water is greater
D. salt water of the sea is denser
Explanation
Why Correct: Sea water contains dissolved salts that increase its density compared to fresh river water, creating greater buoyant force according to Archimedes' principle.
Distractor Analysis: Sea water temperature varies and does not systematically affect buoyancy. Ship speed depends on propulsion and currents, not flotation mechanics. River water has lower density than sea water due to minimal dissolved solids.
Takeaway: Archimedes' principle states the buoyant force equals the weight of fluid displaced, so objects float higher in denser fluids for the same weight.
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Q.20
WBCS Prelims 2003
Viscosity of a liquid
A. Increases with increase in temperature
B. Decreases with increase in temperature
C. Independent of temperature
D. Decreases with increase in pressure
Explanation
Why Correct: Viscosity measures a liquid's internal resistance to flow, which decreases as temperature rises because increased molecular kinetic energy reduces intermolecular forces.
Distractor Analysis: Increases with increase in temperature describes gases, where viscosity rises with temperature due to increased molecular collisions. Independent of temperature applies only to ideal fluids, not real liquids. Decreases with increase in pressure is incorrect for most liquids, though some complex fluids show slight pressure dependence.
Takeaway: For gases, viscosity increases with temperature, creating a common exam contrast with liquids.
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Q.21
WBCS Prelims 2001
A glass bulb is balanced by a brass weight on a sensitive beam balance. Now the balance is covered by a bell-jar which is then evacuated :
A. the beam will continue to remain horizontal
B. the pan containing the bulb will go up
C. the pan containing the bulb will go up or down depending on the degree of vacuum produced
D. the pan containing the bulb will go down
Explanation
Why Correct: Evacuating air removes buoyant force on both objects, but the glass bulb experiences greater buoyancy loss because it has larger volume for the same mass, making it effectively lighter.
Distractor Analysis: Remaining horizontal assumes equal buoyancy effects, but glass has lower density than brass. Going down would occur if brass lost more buoyancy, which is false since brass has smaller volume. Degree of vacuum affects magnitude but not direction of the effect.
Takeaway: Buoyant force equals weight of displaced fluid (Archimedes' principle), so objects with larger volume experience greater buoyancy changes when fluid density changes.
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Q.22
WBCS Prelims 2000
28. A balloon filled with hydrogen bursts on reaching high altitude because.
A. Pressure inside balloon becomes less
B. Pressure inside balloon becomes more
C. Surface of the balloon gets melted
D. It is a natural phenomenon
Explanation
Why Correct: Atmospheric pressure decreases with altitude, causing the higher internal pressure of the hydrogen-filled balloon to expand it beyond its elastic limit, leading to bursting.
Distractor Analysis: Pressure inside the balloon does not decrease with altitude; it remains higher relative to the outside. Balloon surfaces do not melt at high altitudes where temperatures are colder. Bursting is a predictable physical consequence, not a random natural phenomenon.
Takeaway: For every 1000 m increase in altitude, atmospheric pressure drops by about 100 hPa, creating significant pressure differentials for sealed containers.
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