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NEET PHYSICSEasy

The units of angular momentum are:

A

kg m²/s²

B

Joule-s

C

Joule/s

D

kg m s²

Step-by-Step Solution

  1. Definition: Angular momentum (LL) is defined as the moment of momentum. Mathematically, L=r×p=mvrL = r \times p = mvr, where mm is mass, vv is velocity, and rr is the radius .
  2. Dimensional Analysis:
  • Mass (mm): [M][M]
  • Velocity (vv): [LT−1][LT^{-1}]
  • Radius (rr): [L][L]
  • The dimensional formula for angular momentum is [M][LT−1][L]=[ML2T−1][M][LT^{-1}][L] = [ML^2T^{-1}] .
  1. Unit Derivation:
  • The standard SI unit derived from the dimensions is kg⋅m2⋅s−1kg \cdot m^2 \cdot s^{-1}.
  1. Analyzing the Options:
  • Option A (kgm2/s2kg m^2/s^2): This corresponds to Force ×\times Distance, which is Energy (Joule). Dimensions: [ML2T−2][ML^2T^{-2}].
  • Option B (Joule-s): Joule is the unit of energy (kg⋅m2⋅s−2kg \cdot m^2 \cdot s^{-2}). Multiplying by second (ss) gives: (kg⋅m2⋅s−2)⋅s=kg⋅m2⋅s−1(kg \cdot m^2 \cdot s^{-2}) \cdot s = kg \cdot m^2 \cdot s^{-1}. This matches the unit of angular momentum .
  • Option C (Joule/s): This is the unit of Power (Watt).
  1. Conclusion: The correct unit for angular momentum is Joule-second (J⋅sJ\cdot s).
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