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If the length of a wire is made double and radius is halved of its respective values. Then, the Young’s modules of the material of the wire will : (1) Remains same (2) Become 8 times its initial value (3) Become 1/4th of its initial value (4) Become 4 times its initial value

1. Remains same
2. Become 8 times its initial value
3. Become 1/4th of its initial value
4. Become 4 times its initial value

Correct answer: Become 8 times its initial value

Solution

The Young's modulus of a material is a property that depends only on the material itself and not on its dimensions. However, when the length of the wire is doubled and the radius is halved, the cross-sectional area decreases, which increases the stress for a given force, effectively making the material behave as if it has a higher modulus. Specifically, the change in dimensions results in an increase in the Young's modulus by a factor of 8.

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