The Question is from neet-physics units-and-measurement conversion-of-units-for-one-system-to-another, and it was created by the author SUBHANI

Question

Dimensional formula for angular momentum is

SUBHANI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [B]
## CONCEPT FRAMEWORK
	**Primary Concept**: Dimensional Analysis of Angular Momentum
	**Related Topics**: Angular Momentum, Moment of Inertia, Angular Velocity
	**Prerequisites**: Definition of Angular Momentum, Dimensional Formulas for Mass, Length, and Time
## SOLUTION PATHWAY
**Given Information**:
	None explicitly provided, but we need to derive the dimensional formula for angular momentum.
	Angular momentum (L) = Moment of Inertia (I) * Angular Velocity (ω)
**Method & Steps**:
	1. Determine the dimensional formula for Moment of Inertia (I).
		Reasoning: Moment of inertia is given by $I = mr^2$, where m is mass and r is distance.
		Formula/Rule: $[I] = [M][L^2]$
	2. Determine the dimensional formula for Angular Velocity (ω).
		Reasoning: Angular velocity is given by $\omega = \frac{	heta}{t}$, where θ is angle and t is time.
		Formula/Rule: $[\omega] = [T^{-1}]$  (angle is dimensionless)
	3. Determine the dimensional formula for Angular Momentum (L).
		Working: $L = I \omega$,  $[L] = [I][\omega] = [ML^2][T^{-1}] = ML^2T^{-1}$
		Result: $ML^2T^{-1}$
		Verification: The dimensional formula is consistent with the definition of angular momentum.
 ## OPTION ANALYSIS
[A] :x: This is the dimensional formula for energy or torque, not angular momentum.
[B] ✓: This is the correct dimensional formula for angular momentum, derived as $ML^2T^{-1}$.
[C] :x: This is the dimensional formula for linear momentum, not angular momentum.
[D] :x: This is incorrect as it has no mass component and a wrong time component.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Confusing angular momentum with linear momentum. [How to avoid]: Understand the difference between rotational and translational motion.
		2.[Error 2]: Using incorrect dimensional formula for moment of inertia. [How to avoid]: Remember the formula $I=mr^2$ and its dimensional equivalent.
	**Quick Tips**:
		1.[Helpful shortcut]: Remember that angular momentum involves rotational motion and hence a distance squared term ($L^2$).
		2.[Memory aid]: Use L = Iω to derive the dimensional formula.

SUBHANI · Answer

$M{L^2}{T^{ - 2}}$

SUBHANI · Answer

The correct Option is "$M{L^2}\;{T^{ - 1}}$"

SUBHANI · Answer

$ML{T^{ - 1}}$

SUBHANI · Answer

${M^0}{L^2}{T^{ - 2}}$

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