A wire made from some material having radius r and length ℓ and Young modulus Y, then find the Young modulus of another wire made from same material having radius 2r and length ℓ/2.
Question
A wire made from some material having radius r and length ℓ and Young modulus Y, then find the Young modulus of another wire made from same material having radius 2r and length ℓ/2.
Solution
The Young's modulus of a material is a measure of its ability to withstand changes in length when under lengthwise tension or compression. It is a fundamental property of the material and does not change with the dimensions of the object made from the material.
So, the Young's modulus Y of the second wire (with radius 2r and length ℓ/2) made from the same material will be the same as the Young's modulus Y of the first wire (with radius r and length ℓ).
Therefore, the Young's modulus of the second wire is also Y.
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