How much of JEE Main comes from Properties of Solids and Liquids?

JEEGenie estimates about 4% of JEE Main marks come from Properties of Solids and Liquids, based on recent papers. The share varies from year to year.

Which formulas matter most in Properties of Solids and Liquids?

The Properties of Solids and Liquids sheet on this page has 24 formula entries, starting with Stress and Strain, Elastic Moduli, Stress-Strain Curve and Elastic Limit, Poisson's Ratio, Elastic Energy Stored per Unit Volume. Each one comes with when to use it and the trap to avoid.

What topics does Properties of Solids and Liquids cover for JEE?

Properties of Solids and Liquids covers Elasticity, Pressure and Pascal's Law, Surface Tension, Viscosity, Bernoulli's Theorem, Fluid Statics.

How should I revise Properties of Solids and Liquids before the exam?

Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Properties of Solids and Liquids questions on JEEGenie.

How many previous-year questions are there on Properties of Solids and Liquids?

JEEGenie has 784 previous-year questions on Properties of Solids and Liquids, and this page shows a few with worked explanations.

Is practice on Properties of Solids and Liquids free on JEEGenie?

Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.

Properties of Solids and Liquids for JEE Main & Advanced — formulas, what is asked, and traps

JEEGenie estimates about 4% of JEE Main marks come from Properties of Solids and Liquids. This page covers 24 formula entries, each with when to use it, what JEE asks and the traps. A common slip: Confusing stress with force; stress is force per unit area, not just force.

Key points to know

Stress and Strain. Stress is the internal restoring force per unit area, while strain is the fractional deformation. Hooke's law states stress is proportional to strain within the elastic limit.
Elastic Moduli. Young's modulus (Y) for length change, Bulk modulus (B) for volume change, Shear modulus (G) for shape change. They relate stress to strain in different deformation modes.
Stress-Strain Curve and Elastic Limit. The stress-strain curve shows proportional limit (Hooke's law valid), elastic limit (beyond which permanent deformation), yield point, and ultimate tensile strength. Ductile vs. brittle materials differ in plastic region.
Fluid Pressure and Pascal's Law. Pressure in a fluid at rest is transmitted equally in all directions. Pascal's law: pressure applied to an enclosed fluid is transmitted undiminished to every point.
Torricelli's Theorem (Efflux Speed). The speed of efflux of a fluid from an orifice at depth h below the free surface is equal to the speed a body would acquire in free fall from height h.
Viscosity and Newton's Law of Viscosity. Viscosity is the internal friction in a fluid. Newton's law: the shear stress between fluid layers is proportional to the velocity gradient (rate of shear strain).
Surface Tension and Surface Energy. Surface tension (γ) is the force per unit length acting along the surface, or the energy per unit area. It arises due to cohesive forces between molecules.
Calorimetry and Specific Heat. Heat gained or lost by a substance is Q = mcΔT (for temperature change) or Q = mL (for phase change). The principle of calorimetry: heat lost = heat gained in an isolated system.
Degrees of Freedom and Specific Heats of Gases. Degrees of freedom (f) determine the molar specific heats: Cv = (f/2)R, Cp = Cv + R, and γ = Cp/Cv = 1 + 2/f.
First Law of Thermodynamics. Energy conservation: the change in internal energy of a system equals heat added minus work done by the system.

Formula sheet

Name	Formula	When to use
Stress and Strain	$Stress = \frac{F}{A}$ , $Strain = \frac{Δ L}{L}$ (longitudinal), $Shear Strain = \frac{Δ x}{h}$ , $Volumetric Strain = \frac{- Δ V}{V}$	When analyzing deformations in solids under external forces.
Elastic Moduli	$Y = \frac{Tensile Stress}{Longitudinal Strain} = \frac{F / A}{Δ L / L}$ , $B = - \frac{Δ P}{Δ V / V}$ , $G = \frac{Shear Stress}{Shear Strain} = \frac{F / A}{Δ x / h}$	When calculating deformation from applied forces or pressure changes in solids.
Stress-Strain Curve and Elastic Limit	$Elastic limit = maximum stress without permanent deformation$	When interpreting material behavior under load, especially for safety factors.
Poisson's Ratio	$ν = - \frac{Lateral Strain}{Longitudinal Strain} = - \frac{Δ d / d}{Δ L / L}$	When a tensile or compressive force causes both axial and lateral dimensional changes.
Elastic Energy Stored per Unit Volume	$U = \frac{1}{2} \times stress \times strain = \frac{1}{2} Y (strain)^{2} = \frac{(stress)^{2}}{2 Y}$	When calculating energy stored in a stretched wire, compressed spring, or any elastic deformation.
Fluid Pressure and Pascal's Law	$P = \frac{F}{A}$ , $Δ P = ρ g h$ (for a column of fluid), $P = P_{0} + ρ g h$	When analyzing forces on submerged surfaces, hydraulic lifts, or pressure at depth.
Buoyancy and Archimedes' Principle	$F_{b} = ρ_{fluid} \times V_{displaced} \times g$	When an object is floating or submerged in a fluid, to find apparent weight or floating condition.
Equation of Continuity	$A_{1} v_{1} = A_{2} v_{2}$ (for incompressible fluid)	When fluid flows through pipes of varying cross-section, to find velocity changes.
Bernoulli's Equation	$P + \frac{1}{2} ρ v^{2} + ρ g h = constant$	When analyzing fluid flow in pipes, nozzles, Venturi meters, or lift on airplane wings.
Torricelli's Theorem (Efflux Speed)	$v = \sqrt{2 g h}$	When calculating the speed of liquid coming out of a hole in a container.
Viscosity and Newton's Law of Viscosity	$τ = η \frac{d v}{d y}$ , where $η$ is coefficient of viscosity.	When calculating drag force on a moving object in a fluid, or flow through pipes.
Stokes' Law and Terminal Velocity	$F_{d} = 6 π η r v$ , $v_{t} = \frac{2}{9} \frac{(ρ_{s} - ρ_{f}) g r^{2}}{η}$	When a sphere falls through a fluid (e.g., raindrop, ball bearing in oil).
Poiseuille's Law (Laminar Flow in a Pipe)	$Q = \frac{π R^{4} Δ P}{8 η L}$	When calculating flow rate or pressure drop in a pipe for viscous fluids (e.g., blood flow, oil pipelines).
Surface Tension and Surface Energy	$γ = \frac{F}{L}$ , $γ = \frac{Work}{Δ A}$	When analyzing liquid surfaces, bubbles, droplets, capillary rise, or wetting phenomena.
Excess Pressure in Drops and Bubbles	$Δ P_{drop} = \frac{2 γ}{R}$ , $Δ P_{bubble} = \frac{4 γ}{R}$	When calculating the pressure inside a liquid droplet, soap bubble, or air bubble in liquid.
Capillary Rise/Depression	$h = \frac{2 γ \cos θ}{ρ g r}$ , where $θ$ is contact angle.	When calculating the height of liquid in a capillary tube, or the radius from rise height.
Heat Transfer: Conduction, Convection, Radiation	$\frac{d Q}{d t} = - k A \frac{d T}{d x}$ (Fourier's law), $\frac{d Q}{d t} = σ ϵ A T^{4}$ (Stefan-Boltzmann for radiation)	When analyzing heat flow through walls, rods, or from hot objects.
Thermal Expansion of Solids and Liquids	$Δ L = L_{0} α Δ T$ , $Δ A = A_{0} β Δ T$ with $β = 2 α$ , $Δ V = V_{0} γ Δ T$ with $γ = 3 α$	When calculating expansion of rods, sheets, or liquid volumes due to temperature change.
Calorimetry and Specific Heat	$Q = m c Δ T$ , $Q = m L_{f}$ (fusion), $Q = m L_{v}$ (vaporization)	When calculating final temperature or amount of substance after mixing, or heat required for phase change.
Newton's Law of Cooling	$\frac{d T}{d t} = - k (T - T_{s})$	When a hot object cools in a constant-temperature environment (e.g., cup of coffee).
Ideal Gas Equation and Kinetic Theory	$P V = n R T$ , $P = \frac{1}{3} ρ v_{rms}^{2}$ , $\frac{1}{2} m v_{rms}^{2} = \frac{3}{2} k T$	When relating pressure, volume, temperature of gases, or calculating molecular speeds.
Degrees of Freedom and Specific Heats of Gases	$C_{v} = \frac{f}{2} R$ , $C_{p} = \frac{f + 2}{2} R$ , $γ = 1 + \frac{2}{f}$	When calculating heat capacities or adiabatic exponents for gases.
Thermodynamic Processes: Isothermal, Adiabatic, Isobaric, Isochoric	Isothermal: $P V = const$ , $W = n R T \ln (V_{2} / V_{1})$ ; Adiabatic: $P V^{γ} = const$ , $W = \frac{P_{2} V_{2} - P_{1} V_{1}}{1 - γ}$ ; Isobaric: $W = P Δ V$ ; Isochoric: $W = 0$	When analyzing engines, compressors, or any thermodynamic cycle.
First Law of Thermodynamics	$Δ U = Q - W$	In all thermodynamic processes to relate heat, work, and internal energy.

Open the Properties of Solids and Liquids formula page

What JEE asks

Stress and Strain. JEE often asks to identify stress type (tensile, compressive, shear) from a diagram or description, then compute strain using given dimensions.
Elastic Moduli. JEE tests with numerical problems: given force, dimensions, and modulus, find elongation or compression. Also, compare moduli of different materials.
Stress-Strain Curve and Elastic Limit. JEE may show a stress-strain graph and ask to identify points (proportional limit, yield, fracture) or compare ductility/brittleness.
Poisson's Ratio. JEE may ask to find change in diameter or cross-sectional area given axial strain and Poisson's ratio.
Elastic Energy Stored per Unit Volume. JEE often asks to compare energy stored in two wires of different materials or dimensions under same load.
Fluid Pressure and Pascal's Law. JEE tests Pascal's law with hydraulic press problems: given input force and areas, find output force.
Buoyancy and Archimedes' Principle. JEE often asks to find the fraction of volume submerged for a floating object, or the tension in a string holding a submerged object.
Equation of Continuity. JEE tests with numerical: given diameters and velocity at one point, find velocity at another point.
Bernoulli's Equation. JEE often asks to find velocity or pressure at a point given conditions at another point, or to explain phenomena like atomizer, filter pump.
Torricelli's Theorem (Efflux Speed). JEE may ask to find the range of the efflux stream or the time to empty a tank.
Viscosity and Newton's Law of Viscosity. JEE tests with numerical on viscous drag (Stokes' law) or Poiseuille's flow.
Stokes' Law and Terminal Velocity. JEE often asks to find terminal velocity or compare times for spheres of different sizes/materials.
Poiseuille's Law (Laminar Flow in a Pipe). JEE may ask how flow rate changes if radius is halved (factor of 1/16) or length doubled.
Surface Tension and Surface Energy. JEE tests with numerical on excess pressure in bubbles/droplets, or capillary rise height.
Excess Pressure in Drops and Bubbles. JEE often asks to compare pressures in drops of different sizes or find the work done in blowing a bubble.
Capillary Rise/Depression. JEE tests with numerical: given rise height, find surface tension or radius. Also, effect of tube inclination.
Heat Transfer: Conduction, Convection, Radiation. JEE often asks to find temperature gradient or heat current in composite slabs, or compare rates of radiation.
Thermal Expansion of Solids and Liquids. JEE tests with problems on bimetallic strips, expansion of mercury in thermometers, or gaps in rails.
Calorimetry and Specific Heat. JEE often asks to find final temperature when ice is mixed with water, or the amount of steam needed to melt ice.
Newton's Law of Cooling. JEE may ask to find the time to cool from one temperature to another, or to compare cooling rates of different objects.
Ideal Gas Equation and Kinetic Theory. JEE tests with numerical on gas laws, rms speed, or degrees of freedom.
Degrees of Freedom and Specific Heats of Gases. JEE often asks to find γ for a given gas or to compare Cv values.
Thermodynamic Processes: Isothermal, Adiabatic, Isobaric, Isochoric. JEE tests with PV diagrams: identify process, calculate work, heat, or change in internal energy.
First Law of Thermodynamics. JEE often asks to find Q, W, or ΔU given a process on a PV diagram.

Common traps

Confusing stress with force; stress is force per unit area, not just force. Stress and Strain
Forgetting the negative sign in Bulk modulus definition (pressure increase reduces volume). Elastic Moduli
Thinking the proportional limit and elastic limit are the same; they are close but not identical. Stress-Strain Curve and Elastic Limit
Forgetting the negative sign; lateral strain is opposite in sign to longitudinal strain. Poisson's Ratio
Using the formula for plastic deformation; it only applies within elastic limit. Elastic Energy Stored per Unit Volume
Thinking pressure is a vector; it's a scalar (magnitude only, acts perpendicular to surfaces). Fluid Pressure and Pascal's Law
Using the density of the object instead of the fluid in buoyant force calculation. Buoyancy and Archimedes' Principle
Applying to compressible fluids (gases) without considering density changes. Equation of Continuity
Applying Bernoulli's equation to viscous fluids or turbulent flow without modifications. Bernoulli's Equation
Forgetting that the formula assumes the tank is open to atmosphere and the orifice is small compared to tank area. Torricelli's Theorem (Efflux Speed)
Confusing dynamic viscosity (η) with kinematic viscosity (ν = η/ρ). Viscosity and Newton's Law of Viscosity
Using Stokes' law for large velocities or turbulent flow; it's valid only for low Reynolds number (laminar flow). Stokes' Law and Terminal Velocity
Forgetting that the formula is for laminar flow only; turbulent flow has different behavior. Poiseuille's Law (Laminar Flow in a Pipe)
Thinking surface tension and surface energy per unit area are different; they are numerically and dimensionally the same ( $N/m = {J/m}^{2}$ ). Surface Tension and Surface Energy

Topics in Properties of Solids and Liquids

Elasticity
Pressure and Pascal's Law
Surface Tension
Viscosity
Bernoulli's Theorem
Fluid Statics

Previous-year questions on Properties of Solids and Liquids

JEEGenie has 784 previous-year questions on Properties of Solids and Liquids. A few worked examples follow.

Year	Questions
2026	54
2025	47
2024	66
2023	81
2022	71
2021	81
2020	35
2019	70
2018	14
2017	13
2016	16
2015	11
2014	26
2013	14
2012	14
2011	10
2010	9
2009	9
2008	10
2007	6
2006	14
2005	12
2004	20
2003	14
2002	7
2001	3
2000	1
1999	4
1998	3
1997	3
1996	1
1995	1
1994	3
1993	4
1992	3
1991	2
1990	1
1989	3
1988	3
1987	2
1986	4
1985	2
1984	1
1983	4
1982	2
1981	7
1980	1
1979	1
1978	1

Question 1 medium

A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is

α \times 10^{- 6}

J. The value of

α

is _______. (Take surface tension of liquid = 0.08 N/m)

Answer: B

Explanation. Given:

D = 2 mm \Rightarrow R = 1 \times 10^{- 3} m, n = 512, T = 0.08 N/m

Volume conservation:

\frac{4}{3} π R^{3} = 512 \cdot \frac{4}{3} π r^{3}

R^{3} = 512 r^{3} \Rightarrow R = 8 r \Rightarrow r = \frac{R}{8}

Initial surface area:

A_{i} = 4 π R^{2}

Final total surface area:

A_{f} = 512 \cdot 4 π r^{2} = 512 \cdot 4 π {(\frac{R}{8})}^{2} = 512 \cdot 4 π \frac{R^{2}}{64} = 8 \cdot 4 π R^{2}

Change in surface area:

Δ A = A_{f} - A_{i} = 8 (4 π R^{2}) - 4 π R^{2} = 7 (4 π R^{2})

Change in surface energy:

Δ E = T Δ A = 0.08 \times 7 \times 4 π (10^{- 3})^{2}

= 0.08 \times 7 \times 4 π \times 10^{- 6} = 0.08 \times 28 π \times 10^{- 6}

= 2.24 π \times 10^{- 6} \approx 7.04 \times 10^{- 6} J

Thus,

α = 7

B

From NTA/IIT papers: JEE Main 2026 · 2 Apr Shift 1

Question 2 easy

The relationship between the magnetic susceptibility

(x)

and the magnetic permeability

(μ)

is given by : (

μ_{0}

is the permeability of free space and

μ_{T}

is relative permeability)

$X = \frac{μ}{μ_{0}} - 1$
$X = \frac{μ_{r}}{μ_{0}} + 1$
$χ = μ_{r} + 1$
$X = 1 - \frac{μ}{μ_{0}}$

Answer: A

Explanation. We know magnetic permeability

μ = μ_{0} μ_{r}

, and the relation between susceptibility

χ

and relative permeability is

μ_{r} = 1 + χ

. Substitute

μ_{r} = \frac{μ}{μ_{0}}

\frac{μ}{μ_{0}} = 1 + χ

Thus:

χ = \frac{μ}{μ_{0}} - 1

This matches option A. The correct answer is option A.

From NTA/IIT papers: JEE Main 2025 · 2 Apr Shift 1

Question 3 hard

Two large, identical water tanks, 1 and 2, kept on the top of a building of height

H

, are filled with water up to height

h

in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are

t_{1}

and

t_{2}

, respectively. If

H = (\frac{16}{9}) h

, then the ratio

t_{1} / t_{2}

is _____.

Answer: 3

Explanation. We use Torricelli’s theorem. For tank 1, the hole is at height

H

above ground, so the efflux speed at the hole is

v_{1} = \sqrt{2 g (H + h)}

since the water surface is at height

H + h

from ground. For tank 2, the pipe extends to ground level, so the exit speed is

v_{2} = \sqrt{2 g (H + h)}

as well, because the total height from water surface to pipe exit is still

H + h

. However, the key is that the *driving pressure head* for emptying is different: For tank 1, the water level drops from

h

0

above the hole, so the head decreases from

h

0

. For tank 2, the pipe is vertical and full; the water level in the tank drops, but the exit is at ground, so the effective head is

H + h

initially and

H

finally. Time to empty is proportional to

t \propto \frac{volume}{average efflux speed} .

More precisely, for a tank of cross-section

A

and hole area

a

t = \frac{A}{a} \int_{0}^{h} \frac{d y}{\sqrt{2 g (head at that instant)}} .

For tank 1: head at water height

y

above hole is

y

, so

t_{1} = \frac{A}{a \sqrt{2 g}} \int_{0}^{h} \frac{d y}{\sqrt{y}} = \frac{A}{a \sqrt{2 g}} \cdot 2 \sqrt{h} .

For tank 2: head at water height

y

above bottom is

H + y

, so

t_{2} = \frac{A}{a \sqrt{2 g}} \int_{0}^{h} \frac{d y}{\sqrt{H + y}} = \frac{A}{a \sqrt{2 g}} \cdot 2 (\sqrt{H + h} - \sqrt{H}) .

Thus

\frac{t_{1}}{t_{2}} = \frac{\sqrt{h}}{\sqrt{H + h} - \sqrt{H}} .

Given

H = \frac{16}{9} h

\sqrt{H + h} = \sqrt{\frac{16}{9} h + h} = \sqrt{\frac{25}{9} h} = \frac{5}{3} \sqrt{h},

\sqrt{H} = \sqrt{\frac{16}{9} h} = \frac{4}{3} \sqrt{h} .

\frac{t_{1}}{t_{2}} = \frac{\sqrt{h}}{\frac{5}{3} \sqrt{h} - \frac{4}{3} \sqrt{h}} = \frac{1}{\frac{1}{3}} = 3.

3

From NTA/IIT papers: JEE Advanced 2024

Question 4 easy

A small ball of mass

M

and density

ρ

is dropped in a viscous liquid of density

ρ_{0}

. After some time, the ball falls with a constant velocity. What is the viscous force on the ball ?

$F = M g (1 - \frac{ρ_{O}}{ρ})$
$F = M g (1 + \frac{ρ}{P_{o}})$
$F = M g (1 + \frac{ρ_{o}}{ρ})$
$F = M g (1 \pm ρ ρ_{0})$

Answer: A

Explanation. When the ball falls with constant velocity, its acceleration is zero, so the net force on it is zero. The forces acting are: - Weight downward:

M g

- Buoyant force upward:

V ρ_{0} g = \frac{M}{ρ} ρ_{0} g

- Viscous force upward:

F

Balancing forces:

M g = F + \frac{M}{ρ} ρ_{0} g

Solving for

F

F = M g - \frac{M ρ_{0} g}{ρ} = M g (1 - \frac{ρ_{0}}{ρ})

Thus, the viscous force is:

F = M g (1 - \frac{ρ_{0}}{ρ})

Correct option: **A**.

From NTA/IIT papers: JEE Main 2023 · 6 Apr Shift 1

Question 5 medium

A drop of liquid of density

ρ

is floating half immersed in a liquid of density

σ

and surface tension

7.5 \times 10^{- 4}

Ncm

-

1. The radius of drop in

c m

will be : (g = 10 ms

-

$\frac{15}{\sqrt{(2 ρ - σ)}}$
$\frac{15}{\sqrt{(ρ - σ)}}$
$\frac{3}{2 \sqrt{(ρ - σ)}}$
$\frac{3}{20 \sqrt{(2 ρ - σ)}}$

Answer: A

Explanation. For the drop floating half immersed, the forces acting are: 1. **Weight** of the drop:

W = \frac{4}{3} π r^{3} ρ g

2. **Buoyant force** (half the volume submerged in liquid of density

σ

F_{b} = \frac{1}{2} \cdot \frac{4}{3} π r^{3} σ g = \frac{2}{3} π r^{3} σ g

3. **Surface tension force** acting upward along the contact circle of radius

r

F_{s} = 2 π r T

with

T = 7.5 \times 10^{- 4} {N cm}^{- 1} = 7.5 \times 10^{- 2} {N m}^{- 1}

. For equilibrium:

W = F_{b} + F_{s}

\frac{4}{3} π r^{3} ρ g = \frac{2}{3} π r^{3} σ g + 2 π r T

Cancel

π

and divide by

r

\frac{4}{3} r^{2} ρ g - \frac{2}{3} r^{2} σ g = 2 T

\frac{2}{3} r^{2} g (2 ρ - σ) = 2 T

r^{2} = \frac{3 T}{g (2 ρ - σ)}

Substitute

T = 7.5 \times 10^{- 2} {N m}^{- 1}

and

g = 10 {m s}^{- 2}

r^{2} = \frac{3 \times 7.5 \times 10^{- 2}}{10 (2 ρ - σ)} = \frac{2.25 \times 10^{- 2}}{2 ρ - σ}

Since

r

is in cm, convert

r^{2}

from

m^{2}

to cm^{2} (multiply by

10^{4}

r^{2} = \frac{2.25 \times 10^{- 2} \times 10^{4}}{2 ρ - σ} = \frac{225}{2 ρ - σ}

r = \frac{15}{\sqrt{2 ρ - σ}}

Thus, the correct option is:

A

From NTA/IIT papers: JEE Main 2022 · 25 Jul Shift 2

Frequently asked questions

How much of JEE Main comes from Properties of Solids and Liquids?: JEEGenie estimates about 4% of JEE Main marks come from Properties of Solids and Liquids, based on recent papers. The share varies from year to year.
Which formulas matter most in Properties of Solids and Liquids?: The Properties of Solids and Liquids sheet on this page has 24 formula entries, starting with Stress and Strain, Elastic Moduli, Stress-Strain Curve and Elastic Limit, Poisson's Ratio, Elastic Energy Stored per Unit Volume. Each one comes with when to use it and the trap to avoid.
What topics does Properties of Solids and Liquids cover for JEE?: Properties of Solids and Liquids covers Elasticity, Pressure and Pascal's Law, Surface Tension, Viscosity, Bernoulli's Theorem, Fluid Statics.
How should I revise Properties of Solids and Liquids before the exam?: Learn each formula together with its condition of use, read the trap listed beside it, then practise questions and review every mistake. The practice link on this page opens Properties of Solids and Liquids questions on JEEGenie.
How many previous-year questions are there on Properties of Solids and Liquids?: JEEGenie has 784 previous-year questions on Properties of Solids and Liquids, and this page shows a few with worked explanations.
Is practice on Properties of Solids and Liquids free on JEEGenie?: Sign-up is free and includes a 7-day Pro trial. After the trial, free accounts keep a limited daily quota.