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Radius of gyration for metacentric height and time period of oscillation Formula

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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. Check FAQs

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

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

Radius of gyration for metacentric height and time period of oscillation Example

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Here is how the Radius of gyration for metacentric height and time period of oscillation equation looks like with Values.

Here is how the Radius of gyration for metacentric height and time period of oscillation equation looks like with Units.

Here is how the Radius of gyration for metacentric height and time period of oscillation equation looks like.

7.9979 = \frac{(19.18) \cdot \sqrt{0.7 \cdot 9.8066}}{2 \cdot 3.1416}

7.9979m = \frac{(19.18s) \cdot \sqrt{0.7m \cdot 9.8066m/s²}}{2 \cdot 3.1416}

7.9979 = \frac{(19.18) \cdot \sqrt{0.7 \cdot 9.8066}}{2 \cdot 3.1416}

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Radius of gyration for metacentric height and time period of oscillation Solution

Follow our step by step solution on how to calculate Radius of gyration for metacentric height and time period of oscillation?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

k G = \frac{(19.18s) \cdot \sqrt{0.7m \cdot [g]}}{2 \cdot π}

Next Step Substitute values of Constants

∴

k G = \frac{(19.18s) \cdot \sqrt{0.7m \cdot 9.8066m/s²}}{2 \cdot 3.1416}

Next Step Prepare to Evaluate

∴

k G = \frac{(19.18) \cdot \sqrt{0.7 \cdot 9.8066}}{2 \cdot 3.1416}

Next Step Evaluate

∴

k G = 7.99793908859771m

LAST Step Rounding Answer

∴

k G = 7.9979m

Radius of gyration for metacentric height and time period of oscillation Formula Elements

Variables

Constants

Functions

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

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

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

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

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 Radius of gyration for metacentric height and time period of oscillation?

Radius of gyration for metacentric height and time period of oscillation evaluator uses Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi) to evaluate the Radius of Gyration of Floating Body, The Radius of gyration for metacentric height and time period of oscillation 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. Radius of Gyration of Floating Body is denoted by k_G symbol.

How to evaluate Radius of gyration for metacentric height and time period of oscillation using this online evaluator? To use this online evaluator for Radius of gyration for metacentric height and time period of oscillation, enter Time Period of Oscillation of Floating Body (T) & Metacentric Height of Floating Body (GM) and hit the calculate button.

FAQs on Radius of gyration for metacentric height and time period of oscillation

What is the formula to find Radius of gyration for metacentric height and time period of oscillation?

The formula of Radius of gyration for metacentric height and time period of oscillation is expressed as Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi). Here is an example- 7.997939 = ((19.18)*sqrt(0.7*[g]))/(2*pi).

How to calculate Radius of gyration for metacentric height and time period of oscillation?

With Time Period of Oscillation of Floating Body (T) & Metacentric Height of Floating Body (GM) we can find Radius of gyration for metacentric height and time period of oscillation using the formula - Radius of Gyration of Floating Body = ((Time Period of Oscillation of Floating Body)*sqrt(Metacentric Height of Floating Body*[g]))/(2*pi). This formula also uses Gravitational acceleration on Earth, Archimedes' constant and Square Root (sqrt) function(s).

Can the Radius of gyration for metacentric height and time period of oscillation be negative?

No, the Radius of gyration for metacentric height and time period of oscillation, measured in Length cannot be negative.

Which unit is used to measure Radius of gyration for metacentric height and time period of oscillation?

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

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