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Two wires are made of the same material and have the same volume, The first wire has cross-sectional area A and the second wire has cross-sectional area 3A. If the length of the first wire is increased by \Delta l on applying a force F, how much force is needed to stretch the second wire by the same amount ?

  • Option 1)

    4 F

  • Option 2)

    6 F

  • Option 3)

    9 F

  • Option 4)

    F

 

Answers (1)

best_answer

As we have learned

Young Modulus -

Ratio of normal stress to longitudnal strain

it denoted by Y

Y= frac{Normal : stress}{longitudnal: strain}

- wherein

Y=frac{F/A}{Delta l/L}

F -  applied force

A -  Area

Delta l -  Change in lenght

l - original length

 

 

 

F/A=Y\frac{\Delta l}{l}

F=AY\frac{\Delta l}{l}

in second case , F'=A'Y\frac{\Delta l}{l'}

 

volume = constant 

Al = const.\Rightarrow Al = 3Al'

or l'= l/3

F' = Y\frac{3A\Delta l}{l/3}= 9(\frac{YA\Delta l}{l})=9F

 

 

 

 

 

 


Option 1)

4 F

This is incorrect

Option 2)

6 F

This is incorrect

Option 3)

9 F

This is correct

Option 4)

F

This is incorrect

Posted by

Aadil

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