Physics · Mechanical Properties Of Solids · NEET
The required cross-section area for a 10-tonne load gives a rope radius of about 1 cm, and after applying a safety factor of about 10, a radius of about 3 cm. A single solid wire of 3 cm radius behaves almost like a rigid rod. It cannot bend easily over the pulleys and drum of the crane. So instead, many thin wires with the same total area are braided together to keep the strength but gain flexibility.
No. The total load capacity depends only on the total cross-section area of steel and its breaking (or yield) stress, since stress = Force / Area. Braiding does not increase the total area, so it does not increase the maximum load by itself. NCERT lists the reasons as ease of manufacture, flexibility, and strength together. The key new benefit braiding adds over a single rod is flexibility, not extra strength.
You require that the stress stays within the yield strength so the rope does not deform permanently: A >= W / sigma_y = Mg / sigma_y. For M = 10^4 kg, g = 9.8 m/s^2, and mild steel sigma_y = 300 x 10^6 N/m^2, A >= 3.3 x 10^-4 m^2, which is a radius of about 1 cm. This is the minimum. A factor of safety is then applied on top of this.
Real ropes face sudden jerks, wear, corrosion, and load variation, so engineers do not run them at the exact breaking limit. NCERT provides a safety margin of about a factor of 10 in the load, which pushes the recommended radius from about 1 cm up to about 3 cm. This extra thickness is exactly what makes a single solid wire behave like a rigid rod, forcing the braided design.
No. Young's modulus is a property of the material (steel), not of the shape or arrangement. Twisting thin steel wires together does not change the steel's Young's modulus. Braiding only changes how the rope bends and is manufactured, not the intrinsic elastic constants of the material.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
Because a single wire thick enough to lift the load would be almost a rigid rod that cannot bend around pulleys. Braiding thin wires keeps the total steel area (and strength) but adds flexibility and makes manufacture easier.
Using A >= Mg / sigma_y with mild steel yield strength 300 x 10^6 N/m^2, the area is 3.3 x 10^-4 m^2, giving a minimum radius of about 1 cm. With a safety factor of about 10, a radius of about 3 cm is recommended.
Not by itself. Breaking load depends on total cross-section area times breaking stress. Braiding does not add area, so the main gain is flexibility, not extra load capacity.
The yield strength (or breaking stress) of steel. You size the area so the stress from the load stays below the yield strength, then multiply the thickness up using a safety factor.
