TWO close$-$coiled helical springs are compressed between TWO parallel plates by a load of $1$ kN $.$ The springs have a wire diameter of $10$ mm and the radii of coils are $50$ and $75$ mm $.$ EACH spring has $10$ coils, is of the same initial length and both the springs are compressed by the same amount.

Calculate EACH of the following:

$($a$)$ the total deflection;

$($b$)$ the maximum stress in each spring.

Note: Modulus of Rigidity for the spring material $=40G\frac{N}{m^2}$