Question

. A wire of length 2.0 m and radius 1.0 mm is stretched by 25.0 mm on application of a force of 10 3 N. Calculate the Young modulus for the wire.

Answer 1

Answer:

10.49

Explanation:

young modulus=stress/strain

stress=force/area

=103/π/4 ×1

=131.14

strain=dl/l

=25/2

=12.5

131.14/12.5

=10.48

Answer 2

The Young modulus for the wire is $25.48\times 10^{9} \frac{N}{m^{2} }$.

Explanation:

Given :

Length of the wire l= 2 m

Radius of wire r $=1mm=1\times 10^{-3} meter$

Force  F $=10^{3} N$

To Find:

The Young modulus for the wire.

Solution:

Change in length Δl $=25mm =25\times 10^{-3} m$

Radius of wire r $=1mm=1\times 10^{-3} meter$

Area of wire A$=\pi r^{2} =3.14\times (1\times10^{-3} )^{2}$

                                 $=3.14\times 10^{-6} m^{2}$

Force  F $=10^{3} N$

Now, the stress is  $=\frac{F}{A}$

                                $=\frac{10^{3} }{3.14\times10^{-6} } = 318.47\times10^{6}$

Now, the strain is $=\frac{\delta l}{l}$

                              $=\frac{25\times10^{-3} }{2} =12.5\times 10^{-3}$

Now, the young modulus  $Y=\frac{Stress}{Strain}$

                                               $=\frac{318.47\times10^{6} }{12.5\times10^{-3} } =25.48\times 10^{9} \frac{N}{m^{2} }$

Thus,the Young modulus for the wire is $25.48\times 10^{9} \frac{N}{m^{2} }$.

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