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

w_{1} = Additional weight added

Y = Distance of w_{1 }from center

W = Weight of floating ship

## Apparatus Required

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.
- 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 and water level in the tank rises to (Z
_{2}) 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 (w
_{1}) to the horizontal beam of floating ship at a known distance (Y) from thecenter ofbeam . - Now the ship will tilt to 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 usinggiven 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

Tilt angle, =

## 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 =