Question

Dimensional formula for angular momentum.
(A) $M{L^2}{T^{ - 1}}$
(B) $M{L^2}T$
(C) ${M^0}L{T^2}$
(D) ${M^0}{L^0}{T^0}$

Answer 1

Hint We know that the dimensional formula of any terms which depends on the unit of the terms is in the MKS dimensional unit system. The dimensional formula of the angular momentum is determined by using the formula of the angular momentum, then the dimensional unit is determined.
Useful formula
The formula of the angular momentum is,
$L = mvr$
Where, $L$ is the angular momentum of the object, $m$ is the mass of the object, $v$ is the velocity of the object and $r$ is the radius of the object.

Complete step by step solution
The formula of the angular momentum is,
$L = mvr\,.......................\left( 1 \right)$
The SI unit of the mass is given by,
$m = kg$.
The dimensional unit of the mass is given by,
$m = M$.
The SI unit of the velocity is given by,
$v = m{s^{ - 1}}$.
The dimensional unit of the velocity is given by,
$v = L{T^{ - 1}}$.
The SI unit of the radius is given by,
$r = m$.
The dimensional unit of the radius is given by,
$r = L$.
Now, substituting the all the dimensional unit in the angular momentum formula, then the equation (1) is written as,
$L = \left[ M \right] \times \left[ {L{T^{ - 1}}} \right] \times \left[ L \right]$
By multiplying the terms in the above equation, then the above equation is written as,
$L = \left[ {M{L^2}{T^{ - 1}}} \right]$
Thus, the above equation shows the dimensional formula of the angular momentum.

Hence, the option (A) is the correct answer.


Note The students will not get confused with the MKS units and the CGS units. IF suppose the units are given in CGS units, then we must convert the CGS units into the MKS units. After that the dimensional unit is converted from the MKS units. The MKS unit means meter, kilogram and seconds. The CGS units means centimetre, grams and milliseconds.