Problem $1(5$ points$)$

A tensile test is performed on a specimen $15$ mm in diameter and a length of $200$ mm $.$ When an axial load of $300$ N is applied, the length of the specimen increases by $0\mathrm{.}126$ mm $.$

a$)$ What is the modulus of elasticity $\backslash ($ E $\backslash )?$

b$)$ If Poisson's ratio for the specimen is $\backslash ($ v$=0\mathrm{.}4\backslash ),$ what is the final diameter of the specimen?