Question

The ratio of length of two wires of same material is 1:2 and their radii are in the ratio 2:1.When they are loaded equally,the ratio of elongations produced is

Answer 1

Given:

Ratio of length of the two wires = 1:2

Ratio of radii of the two wires = 2:1

To find:

The ratio of elongation produced in the wires.

Solution:

Since the wires are made up if same material, therefore the Young's modulus will be same for both of them.

We know that Y= F. L/ A. l

Where F is applied force which is equal for both wires as load is equal.

L is the initial length of the wire,

l is the change in length (elongation)

A is the cross sectional area of the wire.

l = F. L/ A. Y

Ratio of elongation= l1: l2

l1/ l2 = (F. L1/ A1. Y) / (F. L2/ A2. Y)

= (L1. A2) / (A1. L2)

Since L1/ L2 = 1/2

And A1/ A2 = 2/ 1

That means A2/ A1 = 1/2

Therefore, l1/ l2 = (1/2) * (1/2)

l1/ l2 = 1/4

Therefore the ratio of elongation produced is 1:4.