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Stress Strain Relationship MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

13 Questions around this concept.

Solve by difficulty

One end of a uniform rod of mass M and cross-sectional area A is suspended from rigid support and an equal mass M is suspended from the other end. The stress at the mid-point of the rod will be:

$\mathrm{\frac{2 M g}{A}}$

$\mathrm{\frac{3 M g}{2 A}}$

$\mathrm{\frac{M g}{A}}$

$\mathrm{Zero}$

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Figure shows a graph of the extension $\mathrm{(\Delta l)}$ of a wire of length $\mathrm{1 \mathrm{~m}}$ suspended from the top of a roof at one end and with a load W connected to the other end. If the cross-sectional area of the wire is $\mathrm{10^{-6} \mathrm{~m}^2}$ , the Young's modulus of the material of the wire is

$\mathrm{2 \times 10^{11} \mathrm{~N} / \mathrm{m}^2}$

$\mathrm{2 \times 10^{-11} \mathrm{~N} / \mathrm{m}^2}$

$\mathrm{3 \times 10^{12} \mathrm{~N} / \mathrm{m}^2}$

$\mathrm{3 \times 10^{-12} \mathrm{~N} / \mathrm{m}^2}$

View Solution

Concepts Covered - 1

Stress-strain Curve.

The relation between the stress and the strain or a given material under tensile stress can be plotted on a graph called strain stress curve.

Fig:-A typical stress-strain curve for a metal.

The stress-strain curves vary from material to material. These curves help us to understand how a given material deforms with increasing loads.

When the strain is small (i.e., in region OA) stress is proportional to strain. This is the region where the Hooke’s law is obeyed. The point A is called proportional limit and slope of line OA gives the Young’s modulus (Y) of the material of the wire.
If the strain is increased a little bit, i.e., in the region AB, the stress is not proportional to strain. However, the wire still regains its original length after the removal of stretching force. This behaviour is shown up to point B known as elastic limit or yield-point. The region OAB represents the elastic behaviour of the material of wire.
If the wire is stretched beyond the elastic limit B, i.e., between BC, the strain increases much more rapidly and if the stretching force is removed the wire does not come back to its natural length. Some permanent increase in length takes place.
If the stress is increased further by a very small amount, a very large increase in strain is produced (region CD) and after reaching point D, the strain increases even if the wire is unloaded and ruptures at E. In the region DE, the wire literally flows. The maximum stress corresponding to D after which the wire begins to flow and breaks is called breaking or tensile strength. The region BCDE represents the plastic behaviour of the material of wire.

Types of materials:-

Ductile material:- If the large deformation in the material takes place between elastic limit and fracture point (or)

if the material is having large plastic region, then that material is called ductile material.

Brittle material:- If the material breaks down soon after the elastic limit is crossed, it is called as brittle material.
Elastomers:- These materials only have elastic region (i.e., no plastic region). For example:- rubber