METACENTRIC HEIGHT OF A FLOATING BODY

OBJECTIVE:

To determine the meta centric height and radius of gyration of the given floating body.

EQUIPMENT:

a) Float tank of size 0.8 x 0.8 x 0.3 metre with about 3/4^th full of water.

b) Float (Ship) with arrangement to measure the tilt due to displacement of a small weight.

c) Weights to add to ship:- 500, 300, 200 and 100 gms.

d) Small weights for tilt:- 500, 300, 200 gms.

e) Stop watch.

BASICS:

The float is tilted for an angle of from its horizontal position by placing a small extra weight w on one side of the deck of the float at a distance of ‘x’ cm from the center of the deck. The meta centric height, GM (the distance between center of gravity and the meta center is calculated as

Where

w – the small extra weight in gm added on the deck.

W – the weight of the float in gm.

x- the distance of weight w from the center, measured along

the deck, in cm.

– the angle of tilt measured in degrees.

  and  are the angle of tilt measured, when the weight w is placed on duck at a distance of x cm from center to the left and right sides respectively. The radius of gyration of the float is calculated by noting the time for one free oscillation of the float.

Radius of gyration

Where

T – The mean time for one oscillation in seconds.

GM – Meta centric height in cm at 0^o of tilt (from graph.)

Procedure:

i. Fill the float tank with water for about ¾^th of total height and take the initial reading of height.

ii. Bring the float into horizontal position by screwing the tilt-adjusting nuts inward or outward, so that the plumb line passes through the zero mark of the tilt-measuring device.

iii. Place a small weight w₁ on one side (say left) of the float deck at a distance of x₁(cm) from the center of the deck. Note the shown by the plumb line.

iv. Move the weight w₁ to the other side (right) of the deck for a distance of X₁ cm from the center and note the tilt shown by the plumb line as ?_R⁰.

v. Repeat the steps 3 and 4 for two more distances (x₂cm and x₃cm) and one more small weight w₂, in order to get six sets of readings.

vi. Remove the weight and allow the float to oscillate. Note the time t₁(s) taken for 10 cycles of oscillations.

vii. Repeat step 5 for two times more to get readings t₂ and t_3. Tabulate the readings.

OBSERVATION:

Level of water in the tank – Y₁

Level of water in the tank with vessel – Y₂

Volume of Water displaced = Y₂ – Y₁ x Area of the tank, cm³

Weight of the vessel = Volume of water displaced x Density of water, gms

METACENTRIC HEIGHT

RADIUS OF GYRATION

RESULTS:

INFERENCE:

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