Question

Two wires A and B are of the same material. Their lengths are in the ratio \( 1:2 \) and the diameter is in the ratio \( 2:1 \). If they are pulled by the same force, then increase in length will be in the ratio of

• A. \( 2:1 \)
• B. \( 1:4 \)
• C. \( 1:8 \)
• D. \( 1:2 \)

Hint:

The increase in length is inversely proportional to the cross-sectional area, so smaller cross-sectional area results in a larger increase in length.

Answer 1

The Correct Option is B

Step 1: Understand the relationship.
The increase in length of the wire is proportional to the force applied and inversely proportional to the product of the material's Young's modulus and the cross-sectional area.

Step 2: Apply the formula.
From the formula \( \Delta L = \frac{F L}{A Y} \), where \( F \) is the force, \( L \) is the length, \( A \) is the cross-sectional area, and \( Y \) is the Young's modulus.

Step 3: Compare the two wires.
Since the lengths are in the ratio \( 1:2 \) and the diameters in the ratio \( 2:1 \), the increase in length will be in the ratio \( 1:4 \).