Animated Solution for Physics - Properties of Solids and Liquids: In plotting stress versus strain curves for two materials P and Q, a student by mistake puts strain on the y-axis and stress on the x-axis as shown in the figure. Then the correct statement(s) is (are) :-

The problem of the swapped axes! This is a classic JEE Advanced trap that tests whether you are blindly memorizing shapes of graphs or actually understanding the physical quantities represented on the axes.

When we study elasticity, we are so used to seeing Stress on the y-axis and Strain on the x-axis. It becomes muscle memory. But in this problem, the student has made a "mistake" (or rather, the examiner has set a brilliant trap) by putting Strain on the y-axis and Stress on the x-axis.

This single swap changes how we interpret every single feature of the graph—the slope, the endpoints, and the area. Let's break down the material properties one by one.

Tensile strength is the maximum stress a material can withstand before it fractures or breaks. In a standard graph, we would look at the highest point on the y-axis.

However, since Stress is plotted on the x-axis here, we need to look at how far the curves extend horizontally.

Looking at the endpoints of the curves:

This directly implies that the maximum stress material P can take is greater than that of material Q:

Therefore, material P has more tensile strength than material Q. Option (A) is absolutely correct.

Brittleness

Next, let's talk about ductility. A ductile material can undergo a large amount of plastic deformation before it breaks. In simpler terms, it can be stretched into a long wire. This corresponds to a large maximum strain.

Since Strain is on the y-axis, we need to compare the maximum vertical heights of the two curves.

From the graph, it is visually evident that curve P reaches a much higher point on the y-axis than curve Q:

Because material P can undergo a much larger strain before fracturing, it is more ductile than material Q. Conversely, material Q breaks at a lower strain, making it more brittle. Thus, Option (B) is correct, and Option (C) is incorrect.

Finally, we come to Young's Modulus ($Y$). By definition, Young's Modulus is the ratio of stress to strain in the linear elastic region:

In a standard stress-strain curve, the slope of the linear region is exactly equal to $Y$. But let's calculate the slope ($m$) for our given graph:

Notice that this is the exact reciprocal of Young's Modulus!

Now, let's compare the initial slopes of curves P and Q. Curve P is steeper than curve Q in the linear region, meaning:

Substituting our reciprocal relationship:

When we invert both sides of an inequality (for positive numbers), the inequality sign flips:

So, the Young's Modulus of material P is actually less than that of material Q. This makes Option (D) incorrect.

By carefully respecting the axes provided in the question rather than relying on memorized standard graphs, we successfully deduced that material P is both stronger (higher tensile strength) and more stretchable (more ductile) than material Q, but it has a lower Young's Modulus.

The correct statements are (A) and (B).