Final answer:
The dimensional formula for linear momentum when the fundamental units are Surface tension (S), Moment of Inertia (I), and Planck's constant (h) is S¹/²I¹h⁻¹.
Step-by-step explanation:
The student has asked for the dimensional formula for linear momentum given three fundamental units: Surface tension (S), Moment of Inertia (I), and Planck’s constant (h). We can deduce the relationship based on the given units and their association with linear momentum (p = mv), where m is mass, and v is velocity. Linear momentum has the units of kg · m/s.
By considering the units of the given quantities, we have Surface tension (S) with units equivalent to kg/s² (from the provided equivalence of surface tension), Moment of Inertia (I) with units kg · m², and Planck’s constant (h) with units J·s, which can further be broken down to kg · m²/s. Using dimensional analysis, we can combine these units to get the units kg · m/s for linear momentum as follows:
S = kg/s²
I = kg · m²
h = kg · m²/s
To get the units of linear momentum (kg · m/s), we take the square root of S (S¹/²), multiply it by I (I¹), and divide by h (h⁻¹). Hence, the dimensional formula for linear momentum in terms of S, I, and h is S¹/²I¹h⁻¹.