Metacentric height of Floating Body
Aim: To ascertain the Metacentric height and radius of gyration of specified floating body
Equipment:
- Stopwatch
- Weights for tilt: 200,300, 500 gms
- Float tank of the size 0.8*0.8*0.3
- Ship with the arrangement to ascertain the tilt because of diversion of small weight
Basics:
The float is diverted for an angle of from its level location by insertion of a undersized additional weight w on one face of the deck of the float at a space of ‘x’ cm commencing the middle of the deck. The meta centric height, GM (the space among the main point of gravity and the meta center is assessed as:
Where
w – The small extra weight in gm included on the deck.
W – The weight of the float in gm.
x- The space of weight w from the center, calculated the length of
The deck, in cm.
– The angle of the tilt assessed in degrees.
and are the angle of tilt calculated, when the mass w is positioned on duck at a space of x cm from middle to the left and right sides correspondingly. The radius of gyration of the float is assessed by marking the time period taken for one free fluctuation 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 (specified from the graph.)
Process:
- Fill up the float tank with liquid for approximately ¾thof height and obtain the preliminary analysis of height.
- Keep the float into level position by putting the screw on the tilt- altering the nuts on exterior or interior so that it facilitates the plumb line passes all the way through the zero mark of the tilt-measuring appliance.
iii. Put a undersized weight w_{1} on one side (say left) of the float deck at a space of of x_{1}(cm) from the middle of the deck. Note the exposed by the plumb line.
- Shift the weight w_{1}to the other side (right) of the deck for a distance of X_{1 }cm from the middle and mark the tilt as specified by the plumb line as ?_{R}^{0}.
- Replicate the steps 3 and 4 for two more spaces (x_{2}cm and x_{3}cm) and additional small weight w_{2}, for getting six sets of readings.
Observation:
Level of water in the tank – Y_{1}
Level of water in the tank with vessel – Y_{2}
Volume of Water displaced = Y_{2} – Y_{1} x Area of the tank, cm^{3}
Mass of the vessel = Volume of water displaced x Density of water, gms
Metacentric height
Position of Weight | Sl. No. | Weight, gms | Distance moved in cm | Angle of Tilt | Applied Moment gm-cm | Metacentric Height, MG, cm | Metacentric Height at 0^{o}angle of tilt |
Weight on right side | |||||||
Weight on left side |
Radius of Gyration
Sl. No | Tme for 5 Oscillations. | Period for one Oscillation,
T secs. |
Mean T |
1
2 3 4 5 |
Result:
Inference: