$3\mathrm{.}1)$ Define the following terms using brief notes:

a$)$ Centre of Gravity

$(5$ marks$)$

b$)$ Metacentric Height for a floating body and its implications on the stability of the floating body.

$(10$ marks$)$

$3\mathrm{.}2)$ A crane is used to lower solid concrete blocks into the sea $($see Figure $3).$ Calculate the tension in the rope of the crane due to a rectangular $0\mathrm{.}5m0\mathrm{.}5m2m$ concrete block when it is:

a$)$ Suspended in the air.

$(5$ marks$)$

b$)$ Half$-$immersed in water.

$(5$ marks$)$

Assumptions: The buoyant force in air and the weight of the ropes are negligible

$($The density of sea water $=1030k\frac{g}{m^3}$ and the density of concrete block $=2450k\frac{g}{m^3})$