A uniform cylindrical wire of length 4m and diameter 0.6mm is stretched by a certain force such that it's length is increased by 4mm. If the poission's ratio of the material is 0.3, calculate the change in diameter of the wire.
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The increase in length will be 0.0041 cm
Explanation:
Given,
length = 4 m = 400 cm
diameter = 5 mm = 0.5 cm
=> radius, r = 0.5/2 = 0.25 cm
=> Area = πr² = 3.14 x 0.25 x 0.25 ≈ 0.2 cm²
Force = 5 kg wt = 5000 g x 980 cm/s² = 49 x 10⁵
young's modulus = 2.4 x 10¹² dyne cm²
We know that young's modulus is given by the relation,
Y = (F/A)/(ΔL/L) = FL/AΔL
=> ΔL = FL/YA
= (49 x 10⁵ x 400)/(2.4 x 10¹² x 0.2)
= 0.0041 cm
Hence the increase in length will be 0.0041 cm
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