The three curves shown in the figure represent the trends in Stress-Strain relationship in Bone, Glass and Steel. Which one of the following options correctly matches the curve labels (\(P\), \(Q\), and \(R\)) with these three materials?
Show Hint
Look for a yield plateau (steel), a steep line that snaps suddenly at small strain (glass), and the gentlest slope that still reaches a larger strain (bone).
Step 1: Read what each curve is telling us.
The graph plots stress on the vertical axis against strain on the horizontal axis for three materials, labelled \(P\), \(Q\), and \(R\), each ending at a marked fracture point. To match a curve to a material we look at three things: the initial slope (stiffness, or Young's modulus), whether the curve bends over into a plateau before it fractures (ductility), and how much strain the material can take before it snaps.
Step 2: Recall the property of each material.
Steel is a ductile metal. It has a high stiffness, rises steeply, then yields, that is, it keeps stretching under a nearly steady or slowly rising stress before it finally fractures at a large strain. This gives a curve with a visible bend/plateau and the largest strain to fracture of the three.
Glass is a classic brittle material. It is stiff (steep initial slope) but has almost no ability to deform plastically, so it rises in a straight line and fractures suddenly at a very small strain, with no bend or plateau.
Bone is a natural composite. Its stiffness is lower than both steel and glass, so its initial slope is the gentlest of the three, but it is tougher than glass and can absorb somewhat more strain before it fails, giving it a longer, shallower curve that fractures later along the strain axis than glass does.
Step 3: Match each curve to a material.
Curve \(P\) rises fastest, shows a wavy plateau (a yield-like region) before fracturing at the highest stress and the largest strain. This ductile, high-strength behaviour is characteristic of steel.
Curve \(Q\) is steep and rises without any plateau, breaking suddenly at a moderate stress and a small strain. This straight-line-to-sudden-fracture pattern is characteristic of glass.
Curve \(R\) has the gentlest slope (lowest stiffness) of the three, reaches the lowest peak stress, but its fracture point sits further along the strain axis than \(Q\)'s. This matches bone: less stiff than glass, but able to sustain more strain before breaking.
Step 4: Final Answer.
\(P\) is steel, \(Q\) is glass, and \(R\) is bone.
\[ \boxed{P\text{-Steel; } Q\text{-Glass; } R\text{-Bone}} \]
