JEE Main Pattern Practice Questions

Close the Notes. Start the Clock.

Sections 1 to 12 taught you this chapter — stress and strain, Hooke's law and the whole stress-strain curve, the three moduli, Poisson's ratio and the relations between the constants, strain energy, thermal stress and fatigue, the engineering applications, forty-odd worked problems and a JEE toolkit on top. This section asks one different question: can you use any of it with a timer running?

There is no new theory below. There are 30 single-correct questions built to the exam pattern, and a marking scheme designed to punish the two habits this chapter rewards most cruelly — reaching for a formula before checking which modulus it belongs to, and reading a diameter as though it were a radius.

The rules of engagement

Key Point: This is not a reading exercise. Blank sheet, pen, timer. Attempt all 30 questions in one unbroken sitting, and do not open a single explanation until the last answer is written.

The constants sheet

Every question that needs a number uses these and no others. Copy them to the top of your sheet before you start.

The constants used throughout this drill. Nothing else is needed.

Symbols. $\sigma$ means Poisson's ratio; stress is written $\frac{F}{A}$ and strain is $\varepsilon$. The moduli are $Y$, $G$ and $B$. Compressibility is $\frac{1}{B}$.

What this set covers

That spread mirrors how the paper actually samples this chapter. Young's modulus alone is 6 of the 30, because the loaded wire is the single most-set situation in the whole topic, and it is where an SI slip on mm$^2$ or a diameter read as a radius does the most damage.

The difficulty mix is roughly 25% easy, 45% medium and 30% hard. A handful will feel brutal. They are meant to.

[Exam Tip] That $-1$ is not decoration. Four wild guesses that land one lucky hit earn $4-3 = +1$ mark for four minutes of work — a terrible trade. But a question narrowed to two options returns $\frac{4-1}{2} = +1.5$ marks on average, which is a very good one. Narrow first, then commit. Leave blank only what you could not narrow at all.

[Exam Tip] Before you start, write five lines at the top of your sheet: which modulus — $Y$, $G$ or $B$?, which area?, is that a radius or a diameter?, did I remember the $\frac{1}{2}$?, are my units SI? Those five questions catch the overwhelming majority of the marks lost in this chapter.

Scoring Yourself Honestly

Mark your sheet with the real scheme — $+4$, $-1$, $0$ — and total it. No half marks for "I knew that one really". The number you get is the number that matters.

The bands

Read your own answer sheet

Before you touch a single explanation, sort your mistakes into three piles. This is the most valuable ten minutes in the whole section.

1. Method errors — you reached for $Y$ where the deformation was a shear, or for $B$ where the body was pulled in one direction only. You used the cross-section perpendicular to a tangential force. You applied $\Delta L = \frac{FL}{AY}$ to a wire whose tension varies along its length. These are the expensive ones, because the whole solution is wrong from line one.
2. Execution errors — right method, wrong arithmetic. The classic four in this chapter: a diameter substituted where the formula wanted a radius; mm$^2$ converted as $10^{-3}$ m$^2$ instead of $10^{-6}$ m$^2$; the factor $\frac{1}{2}$ dropped from an energy; and $g$ forgotten, so a mass in kilograms was used as a force in newtons.
3. Reading errors — the question asked for the stress, not the strain; for the energy per unit volume, not the total; for the increase in density, not the decrease in volume; for the load at which the wire breaks, not the load it safely carries.

Key Point: In this chapter pile 2 is unusually fat, and three of its four members are pure unit discipline. $1$ mm$^2 = 10^{-6}$ m$^2$. $1$ cm$^2 = 10^{-4}$ m$^2$. A radius is half a diameter. Write the SI conversion on its own line, every time, and a whole class of lost marks disappears.

The eight habits this set is drilling

• Name the deformation before you name the modulus. Pulled or pushed along one direction: $Y$. Slid or twisted: $G$. Squeezed from every side: $B$. There is no fourth case at this level.
• Name the area before you divide by it. For a longitudinal stress it is the section perpendicular to the force; for a shearing stress it is the face the force acts along.
• Strain has no unit, and stress has the unit of pressure. If your "strain" comes out with a pascal attached, you have divided by the wrong thing.
• Breaking stress belongs to the material, not to the object. Cutting a wire in half changes neither its breaking stress nor its breaking load. What it does change is the extension under a given load.
• A wire is a spring, $k = \frac{YA}{L}$. Wires end to end share the tension; wires side by side share the extension.
• Energy carries a $\frac{1}{2}$, in all three of its forms: $\frac{1}{2}F\Delta L$, $\frac{1}{2}\frac{F}{A}\varepsilon$ per unit volume, $\frac{1}{2}Y\varepsilon^2$, $\frac{\left(F/A\right)^2}{2Y}$.
• Thermal stress is $Y\alpha\,\Delta T$ and contains neither $L$ nor $A$. A short fat rod and a long thin one develop exactly the same stress.
• Check the size of the answer. Strains in metals under safe loads are around $10^{-3}$ or smaller. An elongation of centimetres in a steel wire, or a Poisson's ratio above $0.5$, means you have made an error, not a discovery.

[Exam Tip] Every explanation below is a full step-by-step solution, so this set doubles as revision. Read the explanation even for the questions you got right — several of these have a two-line route and a two-page route, and it is the two-line route you will need in the hall.