Question

The S.I. unit of moment of inertia is:
A. $kg/{{m}^{2}}$
B. $kg{{m}^{2}}$
C. $N/{{m}^{2}}$
D. $N{{m}^{2}}$

Answer 1

Hint: Study about the unit systems used for measurements. Learn the quantities used in the SI unit system. Understand the definition of moment of inertia and try to obtain its mathematical expression. Then from the SI units of its constituents find the unit of moment of inertia.

Complete Step-by-Step solution:
The SI units or the International System of Units is a system of physical units based on the meter, kilogram, second, ampere, kelvin, candela and mole. We use a set of prefixes to express the multiplication or division by power of 10.
Mass is the linear inertia. Moment of inertia is the rotational analog of the linear inertia mass.
Moment of inertia can be defined as the measure of the inertia of a rotational body.
For a point mass the moment of inertia can be defined as the product of the mass of the point object and the square of the perpendicular distance to the axis of rotation of the object.
For the point mass we can mathematically express the moment of inertia as,
$I=m{{R}^{2}}$
Where, $I$ is the moment of inertia, m is the mass of the object and R is the perpendicular distance to the axis of rotation.
The SI unit of mass is kilogram and the Si unit of distance is meter.
So from the mathematical expression we can find out that, the SI unit of moment of inertia will be $\text{kilogram}\text{.mete}{{\text{r}}^{2}}$ or $kg{{m}^{2}}$
The correct option is (B)

Note: For bodies with different shape and size we will find different moments of inertia. But for these values also only the coefficient of $m{{R}^{2}}$will change. Since, coefficients are just numbers, they have no units. So, the unit of moment of inertia will remain the same.