Meta-centric height for time period of oscillation and radius of gyration Calculator

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✖Radius of Gyration of floating body is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass about vertical axis.ⓘ Radius of Gyration of Floating Body [k_G]			+10% -10%
✖Time Period of oscillation of floating body is the time taken by the floating body to complete an oscillation about its axis..ⓘ Time Period of Oscillation of Floating Body [T]			+10% -10%

✖The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body.ⓘ Meta-centric height for time period of oscillation and radius of gyration [GM]

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Meta-centric height for time period of oscillation and radius of gyration

Formula

`"GM" = (4*(pi^2)*("k"_{"G"}^2))/(("T"^2)*"[g]")`

Example

`"0.700361m"=(4*(pi^2)*(("8m")^2))/((("19.18s")^2)*"[g]")`

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Meta-centric height for time period of oscillation and radius of gyration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g])
GM = (4*(pi^2)*(k_G^2))/((T^2)*[g])
This formula uses 2 Constants, 3 Variables

Constants Used

[g] - Gravitational acceleration on Earth Value Taken As 9.80665
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Variables Used

Metacentric Height of Floating Body - (Measured in Meter) - The Metacentric Height of Floating Body is defined as the vertical distance between the center of gravity of a body and the metacenter of that body.
Radius of Gyration of Floating Body - (Measured in Meter) - Radius of Gyration of floating body is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass about vertical axis.
Time Period of Oscillation of Floating Body - (Measured in Second) - Time Period of oscillation of floating body is the time taken by the floating body to complete an oscillation about its axis..

STEP 1: Convert Input(s) to Base Unit

Radius of Gyration of Floating Body: 8 Meter --> 8 Meter No Conversion Required
Time Period of Oscillation of Floating Body: 19.18 Second --> 19.18 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

GM = (4*(pi^2)*(k_G^2))/((T^2)*[g]) --> (4*(pi^2)*(8^2))/((19.18^2)*[g])

Evaluating ... ...

GM = 0.700360798909649

STEP 3: Convert Result to Output's Unit

0.700360798909649 Meter --> No Conversion Required

FINAL ANSWER

0.700360798909649 ≈ 0.700361 Meter <-- Metacentric Height of Floating Body

(Calculation completed in 00.004 seconds)

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Home » Physics » Fluid Mechanics » Fluid Statistics » Buoyancy » Meta-centric height for time period of oscillation and radius of gyration

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PSG College of Technology (PSGCT), Coimbatore

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< 11 Buoyancy Calculators

Meta-centric height in experimental method

Go Metacentric Height of Floating Body = ((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*tan(Angle of Heel)))

Angle of heel for metacentric height in experimental method

Go Angle of Heel = atan((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*Metacentric Height of Floating Body))

Movable weight for metacentric height in experimental method

Go Movable Weight on Floating Vessel = (Metacentric Height of Floating Body*Weight of Floating Vessel*tan(Angle of Heel))/(Distance Travelled by Weight on Vessel)

Time Period of Oscillation of Ship

Go Time Period of Oscillation of Floating Body = (2*pi)*(sqrt((Radius of Gyration of Floating Body^2)/(Metacentric Height of Floating Body*[g])))

Radius of gyration for metacentric height and time period of oscillation

Go Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi)

Volume of body in fluid for metacentric height and BG

Go Volume of Body Submerged in Water = Moment of Inertia of Plain Floating Body/(Metacentric Height of Floating Body+Distance of CG from Center of Buoyancy)

Meta-centric height for time period of oscillation and radius of gyration

Go Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g])

Archimedes Principle

Go Archimedes Principle = Density*Acceleration Due to Gravity*Velocity

Volume of fluid displaced

Go Volume of Fluid Displaced by Body = (Weight of Displaced Fluid)/(Density of Displaced Fluid)

Centre of Buoyancy

Go Centre of Buoyancy for Floating Body = (Depth of Immersed Object in Water)/2

Buoyant Force

Go Buoyant Force = Pressure*Area

Meta-centric height for time period of oscillation and radius of gyration Formula

Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g])
GM = (4*(pi^2)*(k_G^2))/((T^2)*[g])

What is meta-centre?

It is defined as the point about which a body starts oscillating when the body is tilted by a small angle.

What is meta-centric height?

The distance between the meta-centre of a floating body and the center of gravity of the body is called meta-centric height. It is calculated using analytical and theoretical methods.

How to Calculate Meta-centric height for time period of oscillation and radius of gyration?

Meta-centric height for time period of oscillation and radius of gyration calculator uses Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g]) to calculate the Metacentric Height of Floating Body, The Meta-centric height for time period of oscillation and radius of gyration is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre. Metacentric Height of Floating Body is denoted by GM symbol.

How to calculate Meta-centric height for time period of oscillation and radius of gyration using this online calculator? To use this online calculator for Meta-centric height for time period of oscillation and radius of gyration, enter Radius of Gyration of Floating Body (k_G) & Time Period of Oscillation of Floating Body (T) and hit the calculate button. Here is how the Meta-centric height for time period of oscillation and radius of gyration calculation can be explained with given input values -> 0.700361 = (4*(pi^2)*(8^2))/((19.18^2)*[g]).

FAQ

What is Meta-centric height for time period of oscillation and radius of gyration?

The Meta-centric height for time period of oscillation and radius of gyration is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre and is represented as GM = (4*(pi^2)*(k_G^2))/((T^2)*[g]) or Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g]). Radius of Gyration of floating body is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass about vertical axis & Time Period of oscillation of floating body is the time taken by the floating body to complete an oscillation about its axis.

How to calculate Meta-centric height for time period of oscillation and radius of gyration?

The Meta-centric height for time period of oscillation and radius of gyration is given by the relation of oscillation in floating bodies in which the overturning couple is removed. Then the body starts oscillating as if suspended at the meta-centre is calculated using Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g]). To calculate Meta-centric height for time period of oscillation and radius of gyration, you need Radius of Gyration of Floating Body (k_G) & Time Period of Oscillation of Floating Body (T). With our tool, you need to enter the respective value for Radius of Gyration of Floating Body & Time Period of Oscillation of Floating Body and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Metacentric Height of Floating Body?

In this formula, Metacentric Height of Floating Body uses Radius of Gyration of Floating Body & Time Period of Oscillation of Floating Body. We can use 1 other way(s) to calculate the same, which is/are as follows -

Metacentric Height of Floating Body = ((Movable Weight on Floating Vessel*Distance Travelled by Weight on Vessel)/(Weight of Floating Vessel*tan(Angle of Heel)))

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