A rectangular tank is 6m long,4m wide,2m high is flooting in mercury.the center of gravity of the rectangular tank is 1m above the bottom of the tank and depth of immersion of the rectangular tank is 1.6m.the metacentric hight
Answers
answer- 0.7375
Explanation:
Metacentric height = 0.7375 m.
Given :
A rectangular tank is 6m long,4m wide,2m high is floating in mercury.
Center of gravity of the rectangular tank is 1m above the bottom of the tank and depth of immersion of the rectangular tank is 1.6m.
To find :
Metacentric height.
Concept used :
Center of buoyancy = The centroid of the immersed part of floating body.
BM =
GM = BM - BG
GM = Metacentric height.
Where BM = Height of Center of buoyancy and meta center.
I = Area moment of inertia.
V = Volume submerged.
Explanation :
See below attached image.
V = Volume submerged = 1.6 × 4 ×6
= 38.4 m³
I = Area moment of inertia.
=
= 36
BM = = = 0.9375 m
BG = 0.2 m From image attached below.
So GM = BM - BG
= 0.9375 - 0.2
= 0.7375 m.
Therefore, the metacentric height = 0.7375 m.