Question

Unit of moment of inertia in M.K.S system
A. $Kg \times c{m^2}$
B. $Kg/c{m^2}$
C. $Kg \times {m^2}$
D. $Jolule \times m$

Answer 1

Let us first understand the system of units before responding to the query. A system of units is a grouping of units from which other units are derived. This system is also known as an absolute unit system. One of the most widely used systems of units is M.K.S. The metre$\left( m \right)$ is the unit of length in the M.K.S set of units. The kilogram$\left( {kg} \right)$ is a unit of mass. The second $\left( s \right)$ is the unit of time.

Complete step by step solution:
In physics, a moment of inertia is a measurable indicator of a body's rotational inertia—that is, the body's resistance to having its speed of rotation about an axis changed by the application of a torque (turning force). The axis can be internal or external, and it can be set or not. The number of products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis with respect to that axis is known as the moment of inertia (I).Moment of inertia is given as ${\mathbf{I}} = {\text{ }}{\mathbf{M}} \times {{\mathbf{R}}^2}$
[where, I= moment of inertia; M= mass, which is in $\left( {kg} \right)$; and R= distance from the axis, which is in$\left( m \right)$]
M.K.S unit of moment of inertia =$Mass \times {R^2}$
$= kg \times {m^2}$
So, the correct option is: (C) $Kg \times {m^2}$

Note: The MKS (metre, kilogram, second) unit system is the foundation of the SI (System International, or International System) measurement system. As new types of measurement based on MKS emerge in various fields, terms and precise meanings can differ across science and engineering disciplines. The international committee that describes and maintains the SI system of units sorts out these contradictions. As a result, the MKS is the static heart, while the SI is the developing, growing metric measurement method.