Q4 of 39 Page 300

A steel wire and a copper wire of equal length and equal cross-sectional area are joined end to end and the combination is subjected to a tension. Find the ratio of (a) the stresses developed in the two wires and (b) the strains developed. Y of steel = 2 × 1011 N m-2. Y of copper = 1.3 × 10 11 N m-2.

(a) 1

(b)


Here, the wires are of equal length(L) and cross-sectional area(A). Let the force produced by the load across them be F which is same for both the wires.


Young modulus of the steel,


Young modulus of the copper,


(a) Let the stress in steel wire be and that in copper be


Now, and


Hence,


(b) The strain is given by


The strain in the steel wire is


The strain in the copper wire is


hence,



More from this chapter

All 39 →
2

A vertical metal cylinder of radius 2 cm and length 2 m is fixed at the lower end and a load of 100 kg is put on it. Find (a) the stress (b) the strain and (c) the compression of the cylinder. Young modulus of the metal =2 x 1011 N m-2.

 3

The elastic limit of steel is 8 × 108 N m-2 and its Young modulus 2 × 1011 N m-2. Find the maximum elongation of a half-meter steel wire that can be given without exceeding the elastic limit.

 5

In figure (14-E1) the upper wire is made of steel and the lower of copper. The wires have equal cross section. Find the ratio of the longitudinal strains developed in the two wires.


 6

The two wires shown in figure (14-E2) are made of the same material which has a breaking stress of 8 × 108 N m-2. The area of cross section of the upper wire is 0.006 cm2 and that of the lower wire is 0.003 cm2. The mass m1 = 10 kg, m2 =20 kg and the hanger is light. (a) Find the maximum load that can be put on the hanger without breaking a wire. Which wire will break first if the load is increased? (b) Repeat the above part if m1 = 10 kg and m2 = 36 kg.