Question

What is the force required for a steel wire to double it's length when it's area of cross section is one spuare cm. And Young's modules is 200Gpa.

As the length of the wire is doubled the change in length is equal to it's original length.

Answer 1

By the definition of the Young's modulus we have:

$$E=\dfrac{FL_0}{A\Delta L},$$ $$F=\dfrac{EA\Delta L}{L_0}=\dfrac{EAL_0}{L_0}=EA,$$ $$F=2\cdot10^{11}\ \dfrac{N}{m^2}\cdot1\ cm^2\cdot(\dfrac{1\ m}{100\ cm})^2=2\cdot10^7\ N.$$