Question

Radius of gyration is that distance which when squared and multiplied with total mass of the body gives

• A. centre of mass
• B. mass moment of inertia
• C. slenderness ratio
• D. mean distance of mass

Hint:

The radius of gyration ($k$) is a concept used in mechanics to simplify the calculation of the mass moment of inertia ($I$). It represents the effective distance from the axis of rotation at which the entire mass ($M$) of a body could be concentrated to produce the same moment of inertia. The relationship is given by the formula: $I = Mk^2$.

Answer 1

The Correct Option is B

Step 1: Define Radius of Gyration.
The radius of gyration ($k$) is a measure of the distribution of the components of a body around an axis. It is defined such that the moment of inertia ($I$) of the body can be expressed as if its entire mass ($M$) were concentrated at a single distance ($k$) from the axis of rotation.
Step 2: State the formula relating Moment of Inertia, Mass, and Radius of Gyration.
The formula for the mass moment of inertia using the radius of gyration is given by:
$I = Mk^2$
where:
$I$ is the mass moment of inertia
$M$ is the total mass of the body
$k$ is the radius of gyration
Step 3: Interpret the question.
The question asks what is obtained when the radius of gyration is squared and multiplied by the total mass of the body. Based on the formula from Step 2, this product directly yields the mass moment of inertia.
Step 4: Evaluate the options.
Option 1: centre of mass. The center of mass is the average position of all the mass in a system. It is not directly related to the radius of gyration by the given operation.
Option 2: mass moment of inertia. This is correct, as per the definition and formula $I = Mk^2$.
Option 3: slenderness ratio. Slenderness ratio is a parameter in structural engineering, typically defined as the ratio of the effective length of a column to its least radius of gyration. It is not the direct result of the given operation.
Option 4: mean distance of mass. The radius of gyration is related to the distribution of mass, but "mean distance of mass" is not a standard term, and it's not the product $Mk^2$. The final answer is $\boxed{\text{2}}$.