$11\mathrm{.}82$ A $12\mathrm{.}0$ kg mass, fastened to the end of an aluminum rod with an unstretched length of $0\mathrm{.}70$ m$,$ is whirled in a vertical circle with a constant angular speed of $120$ rev$/$min$.$ The cross$-$sectional area of the rod is $0\mathrm{.}014$ cm$2.$ Calculate the elongation of the rod when the mass is

$($a$)$ at the lowest point of the path and

$($b$)$ at the highest point of its path.