A steel bar is $100mm$ long, and has a $20mm$ by $10$ mm cross$-$sectional area. It has Young's modulus of $207$GPa, Poisson's ratio of $0\mathrm{.}26$ and subjected to:

A tensile load of ${10}^{4}N$ along its $20mmx10mm$ face,

ii$.$ A compressive load of ${10}^{5}N$ on its $100mmx20$mmface, and

iii. A tensile load of ${10}^{5}N$ on its $100mmx10mm$ face.

Find:

a$.$ the change in volume of the bar;

b$.$ what the compressive load has to be raised to$,$ so that there is no change from the original volume.