Question

A wire of length l radius r is stretched by a force f and a second wire of same material with kength 2l and radius 2r is stretched with a force 2f then the ratio of elongation in the two wires is

Answer 1

Solution:

Let X be the second wire of the material of the wire,

X = F/πr^2 / l/L = FL / πr^2 l

------------(equation 1)

As both the wires are made up of same material, so their new wire is same.

Let the extension produced in second wire be l'.

Then,

X = 2F/π(2r)^2 / l'/2L = FL / πr^2 l' -------------(equation 2)

Equating (1) and (2), we get

FL / πr^2 l = FL / πr^2 l'

=> l' = l

So, the ratio of elongation in the two wires is 1:1.

Answer 2

Answer:1:1

Explanation:Let X be the second wire of the material of the wire,

X = F/πr^2 / l/L = FL / πr^2 l

------------(equation 1)

As both the wires are made up of same material, so their new wire is same.

Let the extension produced in second wire be l'.

Then,

X = 2F/π(2r)^2 / l'/2L = FL / πr^2 l' -------------(equation 2)

Equating (1) and (2), we get

FL / πr^2 l = FL / πr^2 l'

=> l' = l

So, the ratio of elongation in the two wires is 1:1.