Question

b)
Two wires P and Q are made of same material, the length of both the wires are same but
radius of wire P is 0.1cm and Q is 0.001cm. If same loads are applied on the wires, find
the ratio of increase in their lengths.

Answer 1

Answer

Formula

Y = (F x L)/ (A x ΔL)

• Y is the youngs modulus that depends only on the material
• L is the initial length
• A is the area of cross section
• ΔL is the change in length

Process

It is given that Y,F and L are same.

A$_1$ = $\pi r_1^{2} =\pi (0.1)^{2}=0.01\pi$

A$_2$ = $\pi r_2^{2} =\pi (0.001)^{2}=\pi (0.000001)$

Substituting both of these in the formula:

Y = (F x L)/($0.01\pi$ x ΔL$_1$ )

Y = (F x L)/($0.000001\pi$ x ΔL$_2$ )

Dividing both the equations.

1 = ( $0.000001\pi$ x ΔL$_2$) / ($0.01\pi$ x ΔL$_1$ )

ΔL$_1$  / ΔL$_2$ =  ($0.000001\pi$) / $0.01\pi$

ΔL$_1$  / ΔL$_2$  =  1 / 10000

So, the ratio of increase in their length will be 1 : 10000