Question

A wire whose cross sectional area is A1 is stretched by L1 by a certain weight. How far will a wire of same material and same length and cross section A2 to stretch if same weight is applied to it
(a) A1L1/A2
(b) A2L1/A1
(c) L1
(d) None of the above​

Answer 1

Given:

Cross sectional are of wire = A1

Length stretched = L1

To find:

How far will a wire of same material and same length and cross section A2 to stretch if same weight is applied to it.

Solution:

We know that Youngs modulus = FL₀/AΔL

Where F is the force applied,

L₀ is the initial length

A is the cross sectional area

ΔL is the change in length.

Initially Y = FL₀/ A1L1

When area is A2

L2 = FL₀/ A2 Y

On putting the value of Y we get:

L2 = FL₀A1 L1/A2 F L₀

L2 = A1L1/ A2

Therefore the answer will be option (A) A1 L1/ A2