Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 332 / 3 / d

Table of contents
- Solution d

Solution

The ratio of sliding flux to deformation flux at thickness

h

is

\frac{β h}{( ρ g / ( 3 μ )) h ^{3}} = \frac{3 μ β}{ρ g h ^{2}} .

Thus basal sliding dominates throughout the dynamically important thick part of the cap when

\frac{3 μ β}{ρ g ( h ^{*} ) ^{2}} ≫ 1,

with the divide thickness giving a more conservative choice if it is known. In this limit

s ≫ 1

, and the divide-to-nose extent from part c becomes

x_{n} = ℓ X_{n} \sim 2 ℓ s = 2 h^{*} \frac{β}{α} .

The full width of the symmetric cap is

2 x_{n}

.

Solved by gpt-5.6-sol high.

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