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Copper of fixed volume 'V' is drawn into wire of length 'l'. When this wire is subjected to a constant force'F', the extension produced in the wire is '\Delta l' . Which of the following graphs is a straight line?

 

  • Option 1)

    \Delta l \:versus\:\frac{1}{l}

  • Option 2)

    \Delta l \:versus\:l^{2}

  • Option 3)

    \Delta l \:versus\:\frac{1}{l^{2}}

  • Option 4)

    \Delta l \:versus\:l

 

Answers (1)

As discussed in

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

 

 

 

 v = Al

Y = \frac{F/A}{\Delta l/l} = \frac{Fl}{A.\Delta L} \Rightarrow \Delta l = \frac{Fl}{YA}

\Delta l = \frac{Fl^{2}}{YV} \Rightarrow \Delta l \propto l^{2} 


Option 1)

\Delta l \:versus\:\frac{1}{l}

This solution is incorrect

Option 2)

\Delta l \:versus\:l^{2}

This solution is correct

Option 3)

\Delta l \:versus\:\frac{1}{l^{2}}

This solution is incorrect

Option 4)

\Delta l \:versus\:l

This solution is incorrect

Posted by

Vakul

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