Question

Unit of moment of inertia in MKS system is:

• A. $kg\times c{m}^2$
• B. $kg/c{m}^2$
• C. $kg\times m^2$
• D. $Joule\times m$

Answer 1

The correct option is C

$kg\times m^2$

The explanation of the correct option

Option(C)-

Moment of inertia $\left(I\right)$:

1. The moment of inertia is the resistance of a body to have its rotational speed changed when an external torque is applied to it.
2. Moment of inertia in rotational motion is analogous to mass in translational motion.
3. It is the product of the mass of the body $\left(m\right)$ and the square of distance $\left(r\right)$ of the point where torque is applied from the axis. Mathematically it can be expressed as, $I=mr$.
4. The unit of mass in MKS system is $kg$ and the unit of distance square in MKS system is$m^2$. Therefore, the unit of moment of inertia in the MKS system will be the product of both unit, $kg\times m^2$.
5. Therefore, the unit of moment of inertia is $kg-m^2$.

The explanation of incorrect options

Option(A)-

1. SI unit of distance square is not expressed in $c{m}^2$ in MKS system
2. Therefore this option is incorrect

Option(B)-

1. According to the formula of moment of inertia, unit of mass and distance square would be multiplied and not divided
2. SI unit of distance square is not expressed in $c{m}^2$ in MKS system
3. Therefore this option is not right

Option(D)-

1. Mass of a body is not expressed in joule in MKS system
2. According to the formula of the moment of inertia, it should be a unit of distance square and not distance which is multiplied by the unit of mass in the MKS system.
3. Due to the mentioned reasons,this option is incorrect.

Hence, option C is correct.