Question

A steel wire of 1 m long and 1 mm² cross-sectional area is hung from a rigid end. When a weight of 1 kg is hung from it, then the change in length will be (given Y):

(a) 1/Y​ m
(b) Y/1000​ m
(c) Y/10⁶​ m
(d) Y m

Answer 1

The change in length of the steel wire when a weight of 1 kg is hung from it can be calculated using Hooke's law. The correct answer is (b) Y/1000​ m.

Step-by-step explanation:

To calculate the change in length of the steel wire when a weight of 1 kg is hung from it, we need to use Hooke's law which states that the change in length of an object is directly proportional to the applied force and inversely proportional to the cross-sectional area and Young's modulus of the material.

Given that the cross-sectional area of the wire is 1 mm² and Young's modulus is represented by Y, we can calculate the change in length using the formula: change in length = (applied force * original length) / (cross-sectional area * Young's modulus).

Substituting the given values into the formula, we get the change in length = (1 kg * 1 m) / (1 mm² * Y) = 1000 / Y m. Therefore, the correct answer is (b) Y/1000​ m.