The laboratory procedure to find out the metacentric height of a floating body on water is briefly explained in this article.
A point about which a floating body tries to oscillate is called the
Where, GM = metacentric height
w1 = Additional weight added
Y = Distance of w1 from center
W = Weight of floating ship
Following are the apparatus required to measure metacentric height of a floating body.
- A Tank
- A Floating Ship which contains horizontal beam at its middle and a movable pointer on a graduated scale at the center of horizontal beam.
Test procedure to find metacentric height of a floating body is as follows:
- Take an empty tank and fill it with water up to 2/3rd of its height and note down the height of water level (Z1).
- Now place the floating ship and water level in the tank rises to (Z2) and note it down.
- Adjust the floating ship in such a way that the pointer should show zero reading on the graduated scale.
- After adjusting, add weight (w1) to the horizontal beam of floating ship at a known distance (Y) from the
- Now the ship will tilt to some angle on one side and observe the tilt angle on
graduatedscale and note it down.
- Repeat the same procedure for 4 more times by keeping the load constant and varying the distance or by keeping the distance constant and varying the load.
- In this
casedistance is kept constant as (Y) and weight is varied. Finallycalculate the metacentric height using givenformula.
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
Tilt angle, =
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
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 =