Question $2(20$ marks$)$

$($i$)$ A body weighs $20$ N and $10$ N when weighed under submerged conditions in liquids of relative densities $0\mathrm{.}8$ and $1\mathrm{.}2,$ respectively. Determine

a$.$ Its volume

b$.$ Weight in the air

$[6$ marks$]$

$($ii$)$ A sheet piling holds fresh water and salt water $($relative density $=1\mathrm{.}035)$ on either side of it as shown in Figure $2$a$.$ Find the moment about the base $M$ of the resultant force per unit length of piling.

$[8$ marks$]$

$($iii$)$ Both a gage and a manometer are attached to a gas tank to measure its pressure $($Figure $2$b$).$ If the reading on the pressure gage is $65$ kPa $,$ determine the distance between the two fluids level of the manometer if the fluid is$.$

a$.$ Mercury