Answer: The Young's modulus for the wire is [tex]6.378\times 10^{10}N/m^2[/tex]
Explanation:
Young's Modulus is defined as the ratio of stress acting on a substance to the amount of strain produced.
The equation representing Young's Modulus is:
[tex]Y=\frac{F/A}{\Delta l/l}=\frac{Fl}{A\Delta l}[/tex]
where,
Y = Young's Modulus
F = force exerted by the weight = [tex]m\times g[/tex]
m = mass of the ball = 10 kg
g = acceleration due to gravity = [tex]9.81m/s^2[/tex]
l = length of wire = 2.6 m
A = area of cross section = [tex]\pi r^2[/tex]
r = radius of the wire = [tex]\frac{d}{2}=\frac{1.6mm}{2}=0.8mm=8\times 10^{-4}m[/tex] (Conversion factor: 1 m = 1000 mm)
[tex]\Delta l[/tex] = change in length = 1.99 mm = [tex]1.99\times 10^{-3}m[/tex]
Putting values in above equation, we get:
[tex]Y=\frac{10\times 9.81\times 2.6}{(3.14\times (8\times 10^{-4})^2)\times 1.99\times 10^{-3}}\\\\Y=6.378\times 10^{10}N/m^2[/tex]
Hence, the Young's modulus for the wire is [tex]6.378\times 10^{10}N/m^2[/tex]
