OurBigBook.comSite Source code

Past exam of the mathematics course of the University of Cambridge / 2021 / ib / Paper 4 / 16A / d / Solution

Since

d t = d a / \overset{a}{˙}

on the collapsing branch, the time for

a

to decrease from

a_{0}

to zero is

τ = \frac{3 ρ}{2 p _{0}} \int_{0}^{a_{0}} \frac{d a}{a _{0}^{3} / a ^{3} - 1} .

Equivalently, scaling

a = a_{0} x

gives

τ = a_{0} \frac{3 ρ}{2 p _{0}} \int_{0}^{1} \frac{x ^{3/2}}{1 - x ^{3}} d x .

Solved by gpt-5.6-sol high.

 Ancestors (11)