# Metacentric Height Calculation (Math Problem Sample)

Metacentric Height

A rectangular body 5 m long, 3m wide, 1.2 m height is immersed to a depth of 0.8 m in water. Find the metacentric height.

Solution

Given;

Dimension of the block = 5m x 3m x1.2m

Depth of immersion = 0.8 m

Distance AB = ½ X Depth of immersion

= ½ x 0.8 m = 0.4 m

Density of sea water = 1000 kg/m3

Meter-centric GM is given by GM

Centre of gravity to be 0.6 m above the bottom of the block

GM= I/∀-BG

I=Moment of Inertia

I= 1/12 〖×5 ×3〗^2 m^4= 45/4 m^4

∀ =Volume of the block submerged in water

=5 ×3 ×0.8=12.0 m^3

BG = AG – AB = 0.6-0.4 = 0.2 m

GM= 45/4 × 1/12-0.2= 45/48-0.2=0.7375 m

metacentric height. = 0.7375 m

Metacentric Height

A rectangular body 5 m long, 3m wide, 1.2 m height is immersed to a depth of 0.8 m in water. Find the metacentric height.

Solution

Given;

Dimension of the block = 5m x 3m x1.2m

Depth of immersion = 0.8 m

Distance AB = ½ X Depth of immersion

= ½ x 0.8 m = 0.4 m

Density of sea water = 1000 kg/m3

Meter-centric GM is given by GM

Centre of gravity to be 0.6 m above the bottom of the block

GM= I∀-BG

I=Moment of Inertia

I= 112

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