Question

A light rod of length 200 cm is suspended from the ceiling horizontally by means of two vertical wires of equal length tied to its ends. One of the wires is made of steel and is of cross-section 0.1 sq cm and the other is of brass of cross-section 0.2 sq cm. Find the position along the rod at which a weight may be hung to produce (a) equal stresses in both wires and (b) equal strains in both wires. 

(Y_brass = 10 × 10¹¹ dynes/cm² . Y_steel = 20 × 10¹¹ dynes/cm² .

Answer 1

Let AB be the rod and let C be the point at which the weight is hung.

(a) Stress in steel wire = T₁/0.1

Stress in brass wire = T₂/0.2

As the two stresses are equal,

Taking moments about C,

Equations (i) and (ii) give

(b) Strain = Stress/y = T/Ay

As the strains in both wires are equal,