NCERT Physics Class 11 Exemplar Ch 9 Mechanical Properties of Solids Part 5

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One and More then Answer

Q. 25 (a) A steel wire of mass per unit length with a circular cross section has a radius of The wire is of length when measured lying horizontal, and hangs from a hook on the wall. A mass of is hung from the free end of the wire. Assuming the wire to be uniform and lateral strains longitudinal strains, find the extension in the length of the wire. The density of steel is

Answer: Consider an element dx at a distance x from the load and T (x + dx) are tensions on the two cross sections a distance dx apart, then

Let the length dx at x increase by d, then

Or,

(m is the mass of the wire)

Tension in wire

Tension in Wire

Tension in wire

(b) If the yield strength of steel is , what is the maximum weight that can be hung at the lower end of the wire?

Answer: The maximum tension would be at

The yield forces

At yield

Hence,

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