The Constructor

Determination of Metacentric Height of a Floating Body

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A point about which a floating body tries to oscillate is called the metacenter of that body. The distance between metacenter (M) and the center of gravity (G) of the floating body is known as metacentric height (GM).

The laboratory procedure to find out the metacentric height of a floating body on water is briefly explained in this article.

Metacentric height of a floating body can be found using the following formula:

Where, GM = Metacentric height

w1 = Additional weight added

Y = Distance of w1 from center

W = Weight of floating ship

Determination of Metacentric Height

Apparatus Required

Following are the apparatus required to measure the metacentric height of a floating body.

Fig 1: Metacentric Height Experiment Apparatus

Test Procedure

Test procedure to find metacentric height of a floating body is as follows:

Fig 2: Metacenter(M) Position w.r.t Center of Gravity(G) and Center of Buoyancy (B)


Height of water level in the tank, Z1 =

Height of water level in the tank after placing floating ship, Z2 =

Area of tank, A = length x Width

Metacentric Height Calculations

Difference in height of water levels, Z = Z2 – Z1

Volume of water displaced from the tank due to floating ship, V = Z x A

Weight of floating ship, W = V x Density of water

Formula to calculate metacentric height (GM) of floating body is

Calculate metacentric height for 5 different weights and take the as a result.

Table 1: Metacentric Height of Floating Body Observations

S. No. Weight added to the Floating Ship, w1 Distance of weight from center, Y Tilt angle Metacentric Height (GM)


Metacentric Height of Floating Body, GM =

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