The length of the metallic wire is when the tension in it is It is when the tension is . The original length of the wire will be:
Step 1: Given that:
The length of the first metallic wire is
The tension of the first metallic wire
The length of the second metallic wire is
The tension of the second metallic wire is
Step 3: Draw the required diagram:
Step 2: Formula used:
The general formula of the young modulus in terms of stress and strain
Stress can be calculated as -
where is the force exerted by the object under tension, is the cross-sectional area
Strain will be calculated as-
is the change in length and is the actual length.
Thus putting values we get young's modulus as-
Step 3: Calculating the original length:
Therefore for the first wire's tension :
Using the formula of young's modulus-
For the first metallic wire-
Substituting the known values-
Now for the second wire's tension
Substituting the known values-
Step 4: Now equating the equations:
Therefore, equating equation (1) and equation (2) we get-
Therefore the original length of the wire will be .
Hence, option D is the correct answer.