F: The following process is considered

with

$H_p=\frac{1}{s(s+10)}$

And $H_r$ being a simply proportional controller equal to $K.$ If the closed$-$loop system is to have a damping ratio of $0\mathrm{.}5,$ the gain $K$ must be most nearly

$750$

$10$

$1000$

$100$

$500$