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

GoMeta-centric height in experimental method Formula

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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. Check FAQs

GM = \frac{4 \cdot (π^{2}) \cdot ({k G}^{2})}{(T^{2}) \cdot [g]}

GM - Metacentric Height of Floating Body?k_G - Radius of Gyration of Floating Body?T - Time Period of Oscillation of Floating Body?[g] - Gravitational acceleration on Earth?π - Archimedes' constant?

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

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Here is how the Meta-centric height for time period of oscillation and radius of gyration equation looks like with Values.

Here is how the Meta-centric height for time period of oscillation and radius of gyration equation looks like with Units.

Here is how the Meta-centric height for time period of oscillation and radius of gyration equation looks like.

0.7004 = \frac{4 \cdot ({3.1416}^{2}) \cdot (8^{2})}{({19.18}^{2}) \cdot 9.8066}

0.7004m = \frac{4 \cdot ({3.1416}^{2}) \cdot ({8m}^{2})}{({19.18s}^{2}) \cdot 9.8066m/s²}

0.7004 = \frac{4 \cdot ({3.1416}^{2}) \cdot (8^{2})}{({19.18}^{2}) \cdot 9.8066}

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

Follow our step by step solution on how to calculate Meta-centric height for time period of oscillation and radius of gyration?

FIRST Step Consider the formula

GM = \frac{4 \cdot (π^{2}) \cdot ({k G}^{2})}{(T^{2}) \cdot [g]}

Next Step Substitute values of Variables

∴

GM = \frac{4 \cdot (π^{2}) \cdot ({8m}^{2})}{({19.18s}^{2}) \cdot [g]}

Next Step Substitute values of Constants

∴

GM = \frac{4 \cdot ({3.1416}^{2}) \cdot ({8m}^{2})}{({19.18s}^{2}) \cdot 9.8066m/s²}

Next Step Prepare to Evaluate

∴

GM = \frac{4 \cdot ({3.1416}^{2}) \cdot (8^{2})}{({19.18}^{2}) \cdot 9.8066}

Next Step Evaluate

∴

GM = 0.700360798909649m

LAST Step Rounding Answer

∴

GM = 0.7004m

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

Variables

Constants

Metacentric Height of Floating Body

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.

Symbol: GM

Measurement: LengthUnit: m

Note: Value can be positive or negative.

Formulas to find Metacentric Height of Floating Body

Radius of Gyration of Floating Body

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.

Symbol: k_G

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Gyration of Floating Body

Time Period of Oscillation of Floating Body

Time Period of Oscillation of Floating Body is the time taken by the floating body to complete an oscillation about its axis.

Symbol: T

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Time Period of Oscillation of Floating Body

Gravitational acceleration on Earth

Gravitational acceleration on Earth means that the velocity of an object in free fall will increase by 9.8 m/s2 every second.

Symbol: [g]

Value: 9.80665 m/s²

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other Formulas to find Metacentric Height of Floating Body

Go Meta-centric height in experimental method

GM = (\frac{w 1 \cdot D}{W fv \cdot \tan (θ)})

Other formulas in Buoyancy category

Go Archimedes Principle

A bouy = ρ \cdot g \cdot v

Go Buoyant Force

F buoy = p \cdot A

Go Volume of fluid displaced

V = \frac{W}{ρ df}

Go Centre of Buoyancy

B c = \frac{d}{2}

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

Meta-centric height for time period of oscillation and radius of gyration evaluator 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 evaluate 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 evaluate Meta-centric height for time period of oscillation and radius of gyration using this online evaluator? To use this online evaluator 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.

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

What is the formula to find Meta-centric height for time period of oscillation and radius of gyration?

The formula of Meta-centric height for time period of oscillation and radius of gyration is expressed as Metacentric Height of Floating Body = (4*(pi^2)*(Radius of Gyration of Floating Body^2))/((Time Period of Oscillation of Floating Body^2)*[g]). Here is an example- 0.700361 = (4*(pi^2)*(8^2))/((19.18^2)*[g]).

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

With Radius of Gyration of Floating Body (k_G) & Time Period of Oscillation of Floating Body (T) we can find Meta-centric height for time period of oscillation and radius of gyration using the 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]). This formula also uses Gravitational acceleration on Earth, Archimedes' constant .

What are the other ways to Calculate Metacentric Height of Floating Body?

Here are the different ways to Calculate Metacentric Height of Floating Body-

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

Can the Meta-centric height for time period of oscillation and radius of gyration be negative?

Yes, the Meta-centric height for time period of oscillation and radius of gyration, measured in Length can be negative.

Which unit is used to measure Meta-centric height for time period of oscillation and radius of gyration?

Meta-centric height for time period of oscillation and radius of gyration is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Meta-centric height for time period of oscillation and radius of gyration can be measured.

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