$($a$)$ Show that when a ship is grounded on its centreline during docking, the transverse stability of the ship reduces by: $\frac{PKM}{}$

Where: $$ is the displacement:

KM is the distance from keel to metacentre

$P$ is the upthrust at the point of grounding.

$($b$)$ A vessel $120$ m long and $10000$ tonne displacement enters dock with draughts $7\mathrm{.}6$ m aft and $6\mathrm{.}7$ m forward. $KM=8m$ and $KG=7\mathrm{.}6m.$

MCT $1cm=110tm$ and LCF is at midships.

Calculate the GM at the instant the ship grounds on the blocks.