 Solution

ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2024/paper-1/section-a/1/solution

[γ] = M T^{- 2}

, while

[ρ] = M L^{- 3}

and

[g] = L T^{- 2}

. Consequently

[\frac{γ}{ρ g d ^{n}}] = \frac{M T ^{- 2}}{( M L ^{- 3} ) ( L T ^{- 2} ) L ^{n}} = L^{2 - n} .

Matching the dimension of height gives

2 - n = 1

, so $n = 1$ . Dimensional analysis fixes this exponent but cannot determine a dimensionless prefactor or a contact-angle dependence.

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