determine the metacentric height of a cylinder of 4 m diameter and height of 4m floating in water with its axis vertical, if period of oscillation is 6 seconds

-0.383 m

Explanation:

Diameter of cylinder = 4m  therefore  r = 2

height of cylinder ( H ) = 4 m

specific gravity = 0.6 ( assumed )

depth of immersion = 'h'

Determine the metacentric height

weight of cylinder in water = water displaced

= 0.6 * 1000 * πr^2* H = 1000 * πr^2* h

= 0.6 * 4 = h

∴ h = 2.4 m

hence the depth of center of buoyancy from free space = h /2 = 1.2 m

The metacentric height can be calculated using the formula below

Gm = Io / Vsubmerged  - BG

attached below is the remaining solution

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from wikipedia