The length of a metal wire is 3.75 m when the tension in it is 100 N and is 3.50 m when the tension is 80 N. The natural length of the wire ( in cm) is

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Gremoli9bs · Accepted Answer

Given, Length of wire  when the tension is   100     N  (      l    1    )  =  3.75  m. Length of wire when the tension is   80     N  (      l    2    )  =  3.50  m.  Let us suppose, the natural length of the wire be L m. When tension is 100 N, change in length of wire   (  △  L  )  =      l    1    −  L  =  3.75  −  L   We know that, Young&#039;s modulus   (  Y  )  =            F      ×      L              A      ×      △      L          ⇒  Y  =            100      ×      L              A      ×      (      3.75      −      L      )        ..............(1) Change in length of wire when tension is 80 N Again using the formula of Young&#039;s modulus,  Y  =            F      ×      L              A      ×      δ      L          ⇒  Y  =      80    ×    L        A    ×    (    3.50    −    L    )  ...........(2) From (1) and (2) as the material is same, we can write that,            100      ×      L              A      ×      (      3.75      −      L      )        =            80      ×      L              A      ×      (      3.50      −      L      )          ⇒  350  −  100  L  =  300  −  80  L    ⇒  L  =  2.5  m  o  r  250  c  m

The length of a metal wire is 3.75 m when the tension in it is 100 N and is 3.50 m when the tension is 80 N. The natural length of the wire ( in cm) is

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