Answer
$(a)$ $F=kx$
$(b)$ $k=7.5$
$(c)$ $F=45 N$
Work Step by Step
$(a)$ $F=kx$
Where $F$ is the force needed to stretch spring.
$x$ is difference between stretched and original length.
And $k$ is constant of proportionality; spring constant.
$(b)$
Length in neutral state is $5cm$
$F=30N$
Stretched length is $9cm$
We have to find $k$
$x$ is stretched length, so it equals to $9-5=4cm$
$30=4k$
$k=7.5$
$(c)$ In this case only unknown is $F$
$x=11-5=6cm$
$F=6\times 7.5=45 N$
