The ratio of diameters of two wires of same material is . The length of each wire is . On applying the same load, the increase in the length of the thin wire will be?
times
Explanation for the correct option:
Sep 1: Given
Given, ratio of diameter of the the two wires is and the wires are made of same material.
Let and be the lengths of the two wire.
We have,
Step 2: Formulas used
We know that Young's modulus is given by,
where is Young's modulus, is the force applied and is the area, is the original length of the material and is the change in length after application of load.
Step 3: Solution
We know that the wires are of the same material so their Young's modulus is also same.
Let and be the change in length of the wires and and be their respective areas.
We know that wires are circular. So,
We have,
Since the applied load is same,
We know,
So,
Therefore, the increase in the length of the thin wire is times.
Hence, option D is correct.