A steel wire is streached by a certain amount under a load. If the load and radius both are to four times find the stretch caused in wire
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Young's modulus or Young modulus is a mechanical property that measures the stiffness of a solid material.
It defines the relationship between stress and strain in a material in the linear elasticity. It is constant for a given material.
Young's modulus,
Υ = (W*L)/(A*l)
W = Weight / Force or Load
L = Length of the wire
A = Cross section area of the wire (πr² with r as radius of wire cross section)
l = Elongation.
∴ Elongation,
l = W*L/(A*Υ)
= W*L/( Υ *πr²)
When both load and radius are increased to four times,
r = 4r, W = 4W
the elongation becomes
New l = 4W×L/( Υ *π(4r)²) = WL/( Υ *4πr²)=l /4.
The elongation becomes 1/4 th of the original elongation.
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