Question

If $J$ and $E$ represent the angular momentum and rotational kinetic energy of a body then $\frac{J^2}{2E}$ represents which of the following physical qunatity.

• A. Moment of couple
• B. Moment of force
• C. Moment of inertia
• D. Force

Answer 1

The correct option is C Moment of inertia

$J=M^1{L}^2{T}^{-1}$
$E=M^1{L}^2{T}^{-2}$

$\frac{J^2}{2E}=\frac{(M^1{L}^2{T}^{-1}{)}^2}{2\left(M^1{L}^2{T}^{-2}\right)}=\frac{M^2{L}^4{T}^{-2}}{M^1{L}^2{T}^{-2}}={ML}^2{T}^0$

Moment of inertia $=M{r}^2=M^1{L}^2$