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The dimensional formula of angular momentum is

Asked in CBSE AIPMT 1988 · Dimensional formula of a named quantity

(1) [ML²T⁻²]
(2) [ML⁻²T⁻¹]
(3) [MLT⁻¹]
(4) [ML²T⁻¹]

Answer: (4) [ML²T⁻¹]

Step-by-step solution

Idea: angular momentum is the moment of linear momentum about a point.

L=m v r

[L]=[M][LT⁻¹][L]

[L]=[ML²T⁻¹]

Check with L=Iω: [ML²][T⁻¹] gives the same.

Why the other options are wrong

(1) comes from these are the dimensions of torque or work; angular momentum has one power of time more
(2) comes from the length exponent has the wrong sign, which no step in L=mvr can produce
(3) comes from these are the dimensions of linear momentum, with the lever arm not included

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