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

w_{1} = Additional weight added

Y = Distance of w_{1 }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.

- 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.
- Weights

### Test Procedure

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

- Take an empty tank and fill it with water up to 2/3
^{rd}of its height and note down the height of water level (Z_{1}). - Now place the floating ship in the tank and note down the rise in the water level (Z
_{2}). - Adjust the floating ship in such a way that the pointer should show zero reading on the graduated scale.
- After adjusting, add weight (w
_{1}) to the horizontal beam of floating ship at a known distance (Y) from thecenter of the beam . - Now the ship will tilt at some angle on one side and observe the tilt angle on
graduated scale 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
case, distance is kept constant as (Y) and weight is varied. - Finally, calculate the metacentric height using the
given formula.

### Observations

Height of water level in the tank, Z_{1} =

Height of water level in the tank after placing floating ship, Z_{2} =

Area of tank, A = length x Width

### Metacentric Height Calculations

Difference in height of water levels, Z = Z_{2 }– Z_{1}

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, w_{1} | Distance of weight from center, Y | Tilt angle | Metacentric Height (GM) |

1 | ||||

2 | ||||

3 | ||||

4 | ||||

5 |

### Result

Metacentric Height of Floating Body, GM =