An experiment is conducted to determine Young’s modulus (Y ) of a material using the concept of elasticity. A wire of length L = 2 m and diameter d = 0.5 mm is subjected to a load F = 500 N, resulting in an extension e = 1.5 mm. Calculate Young’s modulus of the material.
4.4 * 1012 N/m2
3.4 * 1012 N/m2
3.4 * 1011 N/m2
4.4 * 1011 N/m2
Given values:
Length of the wire (L) = 2 m
Diameter of the wire (d) = 0.5 mm
Load applied (F) = 500 N
Extension (e) = 1.5 mm
Step 1: Calculate the cross-sectional area (A) of the wire using its diameter:
Step 2: Calculate the stress () in the wire:
Step 3: Calculate the strain () in the wire:
Step 4: Calculate Young's modulus (Y) using the relationship between stress and strain:
Step 5: Substitute the values and calculate Y:
Step 6: Calculate the areas (A) in m2 by converting d to meters:
Step 7: Substitute the values into the formula for Y:
Step 8: Calculate Y:
Young's modulus of the material is 3.4 * 1012 N/m2.
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