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

a$)$ Centre of Gravity

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

floating body.

$3\mathrm{.}2)$ 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.

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

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

$($The density of sea water $=10\mathrm{.}30k\frac{g}{m^2}$ and the density of concrete block $=2450k\frac{g}{m^2})$

Useful Equations:

$F_{T\text{a}\text{i}\text{r}}=W=p_{\text{c}\text{o}\text{n}\text{c}\text{r}\text{a}\text{t}\text{e}}gV$