Problem No$.2$: A spring is extended by $30$ mm when a force of $1\mathrm{.}5$ N is applied to it$.$

$($a$)$ Calculate the energy stored in the spring when hanging vertically supporting a mass of $0\mathrm{.}20$ kg if the spring was unstretched before applying the mass.

$($b$)$ Calculate the loss in potential energy of the mass. $[$Hint: Hooke's law$]$