A cylindrical rod $($radius $=50$mm $)$ made of only steel is fixed at point A$.$ There is an external force of $10$ kN applied at point B$.($a$)$ Find the change in length of the steel rod. Also, $($b$)$ find the final diameter of the steel rod due to Poisson's effect. Note: Young's Modulus $($E$)$ of Steel is $200$ GPa and Poisson's ratio is v$=0\mathrm{.}3.$

Solve using the Hooke's law and Poisson's ratio