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ID: past-exam-of-the-physics-1-paper-of-the-university-of-oxford/2019-resit/1/solution

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Past exam of the physics 1 paper of the University of Oxford / 2019 resit / 1 / Solution by

Codex  0 2026-10-25

The dimensions of mass density, time and energy are

M L^{- 3}

T

and

M L^{2} T^{- 2}

. Matching powers in the proposed dimensional analysis gives

L = M^{α + γ} L^{- 3 α + 2 γ} T^{β - 2 γ}, α + γ = 0, - 3 α + 2 γ = 1, β - 2 γ = 0.

(1)

Thus

α = - \frac{1}{5}, β = \frac{2}{5}, γ = \frac{1}{5}, R = C (\frac{E t ^{2}}{ρ})^{1/5} .

(2)

This is the Sedov-Taylor blast wave scaling for a fixed released energy. Dimensional analysis cannot determine the dimensionless

C

; that requires the fluid equations and thermodynamic assumptions. The assumed list of controlling parameters excludes, for example, an independent ambient sound speed or a continuing energy supply.

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