Physics · Mechanical Properties Of Solids · NEET
No. Breaking stress is a property of the MATERIAL only, like density. A thin steel wire and a thick steel wire have the SAME breaking stress. What changes is the breaking FORCE: breaking force = breaking stress x area. So a thicker wire (bigger area) can hold more load, but the stress at which it fails is the same. NEET loves this: if they double the radius, area becomes 4 times, so breaking force becomes 4 times, but breaking stress stays the same.
Breaking force is the actual load (in newtons) that snaps the wire. Breaking stress is that force divided by the cross-section area (in N/m^2 or Pa). Force depends on the wire's size; stress does not. Formula: Breaking stress = Breaking force / Area. Always divide by area to compare different-sized wires fairly.
NCERT crane example: a 10-tonne load needs a steel rope of only about 1 cm radius at the yield limit. But real ropes must survive sudden jerks, rust, defects and repeated loading (fatigue). So a safety factor of about 10 in load is used, giving a rope of about 3 cm radius. Factor of safety = breaking (or yield) stress / working stress. A value of 10 means the rope is loaded to only 1/10th of its breaking capacity.
No, but NEET often uses them loosely. Yield strength is the stress where permanent (plastic) deformation begins. Ultimate tensile strength is the maximum stress on the graph. Breaking stress (fracture point) is where it actually snaps, usually a little after the ultimate point. For safe design NCERT uses the YIELD stress, because we don't want any permanent stretch, not just avoid snapping.
Cutting a wire in half changes its LENGTH, not its area. Breaking stress depends on material (unchanged) and breaking force depends on area (unchanged). So neither the breaking stress nor the breaking force changes when you shorten a wire. Only elongation and stiffness (k) change with length.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Same as any stress: N/m^2 or pascal (Pa). Typical steel breaking/yield stress is of the order of 10^8 to 10^9 Pa.
Yes. It is a ratio of two stresses (breaking stress / working stress), so it has no units. A factor of safety of 10 means working stress is one-tenth of breaking stress.
Working stress (or permissible stress) is the maximum stress a material is allowed to experience in normal safe use. It equals breaking stress divided by the factor of safety.
Maximum load = Breaking stress x Cross-section area. Example: breaking stress 300 x 10^6 N/m^2 and area 1 x 10^-4 m^2 gives a maximum force of 3 x 10^4 N (about 3 tonnes).
NCERT: a single 3 cm radius steel wire would be almost a rigid rod. Braiding many thin wires (like a pigtail) gives the same strength but adds flexibility and easier manufacture. This is the topic of the next page.
