A uniform metallic wire is elongated by when subjected to a linear force . The elongation, if its length and diameter is doubled and subjected to the same force will be ________.
Step 1. Given Data:
Change in length on applying force is,
Step 2. Solving using Young's modulus relation
Young's modulus,
[, is the radius]
Where, the is area and is the length of wire, is the force applied.
Step 3. Finding the new area
Now, when the length is doubled to and the new diameter, is doubled to, the radius changes to and the area changes to .
By using the formula of area,
[The diameter is twice the radius.]
[]
Step 4. Finding the change in the new length,
Putting the value of the new area, in we get,
Since, the material is the same for both the lengths hence, will be the same even if a change in dimension occurs.
From equation and equation we can write,
Hence, the correct answer is .