# Solving Numerical problem based on Young modulus

Let’s solve numerical problems based on the Young modulus formula.

Young’s Modulus is the ratio of Longitudinal Stress and Longitudinal Strain. If it’s designated with Y then

Y = Longitudinal Stress / Longitudinal Strain = (F/A)/( ΔL /L) = (FL)/(A ΔL )

## Numerical Problem based on Young modulus with solution

#1 Question

A force of 250N is applied to a steel wire of length 1.5m and diameter 0.60 mm.
Calculate the extension of the wire.
(Young modulus for mild steel = 2.1 x 1011 Pa)

Solution

Diameter = d = 0.6 mm = 0.6 x 10-3 m
Cross-sectional area of the wire A= π.(d/2)2= (22/7) . ( 0.6 x 10-3/2)2 = 2.83 x 10-7 m2

Force F = 250 N

L = 1.5 m

extension of the wire = ΔL = ?

Young modulus Y = 2.1 x 1011 Pa

Using the formula of Young modulus:
Y= (FL)/(A ΔL)

ΔL = (FL)/(A Y)

ΔL = (250 x 1.5)/( 2.83 x 10-7 x 2.1 x 1011 ) = 6.3 x 10-3 m = 6.3 mm

Hence, the extension of the wire = 6.3 mm

Solving Numerical problem based on Young modulus
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