A ball of mass 100 g is dropped from a height $h = 10 \mathrm {~cm}$ on a platform fixed at the top of a vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac { h } { 2 }$. The spring constant is $\_\_\_\_$ $\mathrm { N } \mathrm { m } ^ { - 1 }$\\
(Use $g = 10 \mathrm {~m} \mathrm {~s} ^ { - 2 }$)