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  • Two wires A and B are of same length . The diameter are in the ratio 1 : 2 and the youngs modulus are in the ratio of 2 : 1 . If they are pulled by the same force then their elongation will be in r

Two wires A and B are of same length . The diameter are in the ratio 1 : 2 and the youngs modulus are in the ratio of 2 : 1 . If they are pulled by the same force then their elongation will be in ratio 

Option: 1

4 : 1 


Option: 2

1 : 4 


Option: 3

1 : 2 


Option: 4

2 : 1 


Answers (1)

best_answer

As we learned 

Young Modulus -

The ratio of normal stress to longitudinal strain

it denoted by Y

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

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

i.e

F -  applied force

A -  Area

\Delta l -  Change in length

L- original length

So

 

 \frac{\Delta l}{l}= \frac{F}{AY}\: \: or \: \: \Delta l= \frac{Fl }{\pi r^2Y}\\\\\\ \frac{\Delta l_1}{\Delta l_2} = \frac{Y_2r_{2}^{2}}{Y_1r_{1}^{2}}= \frac{1}{2}\times \frac{4}{1}= 2: 1

 

Posted by

manish

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