Question

A mass of 2kg is attached to the end of a vertical wire of length 2m and diameter 2mm extend the wire by 1mm. Calculate the young modulus of the wire

Answer 1

Answer:

12732.4 N/mm²

Explanation:

young modulus of the wire y = stress/strain

y = 20/π ÷ 1/2×10³ = 40000/π N/mm² = 12732.4 N/mm²

Answer 2

Answer:

A mass of 2kg is attached to the end of a vertical wire of length 2m and diameter 2mm extend the wire by 1m, the young modulus of the wire is $Y=4.24*10^{6}$

Explanation:

• The Young's modulus (Y) is the ratio of longitudinal stress by corresponding strain

                   $Y= stress /strain$

• The stress is the force by area and the strain is the ratio of change in length divided by its original length

                  $stress=F/A$

                  $strain=l/L$

From the question,

diameter of the wire $d=2mm=2*10^{-3}m$

the radius $r=d/2=10^{-3}m$

cross-sectional area $A=\pi r^{2} =3.14*10^{-6}m^{2}$

here force is due to the weight of the body suspended at the end

weight $W=mg$

mass of the body $m=2kg$

acceleration due to gravity $g=10m/s^{2}$

⇒ weight $W=2*10=20N$

the stress is $=\frac{20}{3.14*10^{-6} } =6.36*10^{6} N/m^{2}$

the length of the copper wire $L=2m$

extension produced $=1m$

new length $l=2+1=3m$

so the strain is $3/2=1.5$

put all the given values

the young's modulus  $Y=\frac{6.36*10^{6} }{1.5}=4.24*10^{6}m$