Q1.Two wires of same length & materials but different radii are suspended from a rigid support.both carry the same load.Will the stress,strain & extension in them be same or different.Justify your answer.

Q2.A wire stretches by a certain amount under a load.If the load & radius both are increased to 4 times.Find the strecth caused in the wire.

(a)

The stress is given as

σ = F/A

so it dependent upon area of cross-section or radius of the wire. Thus it will be different in two cases.

Now strain and extension depend upon the initial and final lengths of the wire also the Young's Modulus. Now, as these quantities are same for both wire thus strain and extension will be same as well.

we know that the Young's Modulus is given as

Y = F.l / A.dl

here

F = load

L = initial length

A = initial area of cross-section = πr²

dl = increase in length or extension

now the extension will be given as

dl = F.l / A.Y

so, as both F and r are increase four times

F' = 4.F

r' = 4.r

so,

A' = πr'² = π(4r)² =16.πr² = 16.A

so, new extension will be

dl' = F'.l / A'.Y

or

dl' = 4F.l / 16A.Y = (1/4).(F.l / A.Y)

thus, we get

dl' = (1/4).dl

so the new extension decreases four times.