Question

The dimensions of angular momentum/ magnetic moment are
$\begin{align}
  & \left( A \right)\left[ M{{A}^{-1}}{{T}^{-1}} \right] \\
 & \left( B \right)\left[ {{M}^{-1}}A{{T}^{1}} \right] \\
 & \left( C \right)\left[ MA{{T}^{-1}} \right] \\
 & \left( D \right)\left[ M{{A}^{-1}}T \right] \\
\end{align}$

Answer 1

Hint: Angular momentum is said to be a rotational equivalent of linear momentum. It is a conserved quantity, i.e. for any closed system total angular momentum remains constant. Magnetic moment is the strength of the magnets that produce the magnetic field around it.

Formulas used:
Angular momentum calculated as:
$=I\omega $
Magnetic moment: $\tau =m\times B$
Where:
$I$- rotational inertia
$\omega $- angular velocity
$\tau $- torque acting on dipole
$m$- magnetic moment
$B$- external magnetic field

Complete step by step answer:
And the dimensional formula for angular momentum is defined as: $\left[ {{M}^{1}}{{L}^{2}}{{T}^{-1}} \right]$
The magnetic momentum’s dimensional formula is: $\left[ A{{L}^{2}} \right]$
So, the dimension for angular momentum/magnetic moment:
$\begin{align}
  & =\dfrac{\left[ {{M}^{1}}{{L}^{2}}{{T}^{-1}} \right]}{\left[ A{{L}^{2}} \right]} \\
 & =\left[ M{{A}^{-1}}{{T}^{-1}} \right] \\
\end{align}$

So, the correct option for this is option (A).

Additional Information:
when there's no torque applied, the perpendicular velocity of the body will depend on the radius of the circle. I.e. the space from the middle of mass of the body to the middle of the circle. Thus,
for a shorter radius, velocity is going to be high.
for a better radius, velocity is going to be low.
as to conserve the momentum of the body.

Note:
Constant numbers in formulae do not have a dimension and are ignored. only physical quantities with the same dimensions may be added or subtracted. Magnetic moments can also be suggested in terms of torque and moment. Conferring thereto, the torque is measured in Joules ($J$) and therefore the magnetic flux is measured in tesla ($T$) and thus the unit is $J{{T}^{-1}}$.