Question

The following four wires A, B, C and D have their lengths, radii and Young’s modulus as tabulated below.

Wire	Length	Radius	Young’s Modulus
A	L	r	3Y
B	2L	2r	2Y
C	4L	4r	Y/2
D	6L	3r	Y/6

When subjected to same load; the maximum extension will be observed in wire

(1) A

(2) B

(3) C

(4) D

Answer 1

(4) D

We have extension = ΔL = FL/AY = FL/πr²Y

For the same load extension in proportional to L/r²Y. 

In other words the extension depends on the value of L/r²Y of the wires. We have, the values of L/r²Y in the following table.

As the value is maximum for D; the extension will also be maximum in D.