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If surface tension (S), M moment of Inertia (I) and Plank's constant (h), were to be taken as the fundamental units, then the dimensional formula for linear momentum would be
- S³/2 I¹/2 h⁰
- S¹/2 I¹/2 h⁻¹
- S¹/2 I³/2 h⁻¹
- S¹/2 I¹/2 h⁰
Correct answer: S¹/2 I¹/2 h⁰
Solution
Write p=S^a I^b h^c with [M L T^-1]. Matching M: a+b+c=1; L: 2b+2c=1; T: -2a-c=-1 gives a=1/2, b=1/2, c=0. So momentum = S^(1/2) I^(1/2) h^0.
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