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Question

A force F doubles the length of wire of cross-section ‘a’. What is the Young modulus of wire ?


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Solution

Step 1: Given data

According to the question, when a force is applied to the wire, then the length of the wire doubles

So, a change in the length of the wire is given as L=2LL=L.

Step 2: Formula used

Y=Fa×LL

F is the force applied on the wire, a is the area of the cross-section of the wire, L is the initial length of the wire (before applying the force), L is the change in the length of the wire on applying a force and ‘Y’ is the young modulus of elasticity of the wire.

Step 3: Calculating the Young modulus of wire

So, a change in the length of the wire is given as L=2LL=L.
Now, substituting L=L in the equation Y=Fa×LL to determine the expression for the young modulus of elasticity of the wire.

Y=Fa×LLY=Fa×LLY=Fa

Hence, the young modulus of the wire such that it elongates when a force (F) is applied on it is Fa


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