Two wires A and B are of the same material. Their lengths

Two wires A and B are of the same material. Their lengths are in the ratio 1 : 2 and the diameter are in the ratio 2 : 1. If they are pulled by the same force, then increase in length will be in the ratio

We know that Young's modulus

Y =	F	×	L
	πr²		l

Since Y, F are same for both the wires, we have,

	1		L₁	=	1		L₂
	r₁²		l₁		r₂²		l₂

or,	l₁	=	r₂² × L₁	=	(D₂/2) × L₁	mv²
	l₂		r₁² × L₂		(D₁/2) × L₂

or,	l₁	=	D₂² × L₁	=	D₂ L₁	×	L₂	=	1
	l₂		D₁² × L₂		(2D₂)²		2L₂		8

So, l₁: l₂ = 1 : 8