DP Physics (last assessment 2024)

Question 19M.3.HL.TZ2.b

Date	May 2019	Marks available	[Maximum mark: 2]	Reference code	19M.3.HL.TZ2.b
Level	HL	Paper	3	Time zone	TZ2
Command term	Show that	Question number	b	Adapted from	N/A

[Maximum mark: 2]

19M.3.HL.TZ2.b

The homogeneous model of the universe predicts that it may be considered as a spherical cloud of matter of radius r and uniform density ρ. Consider a particle of mass m at the edge of the universe moving with velocity v and obeying Hubble’s law.

At critical density there is zero total energy. Show that the critical density of the universe is: ${{\text{r}}_c} = \frac{{3H_0^2}}{{8\pi G}}$ .

[2]

Markscheme

substitutes H₀r for v ✔

«total energy = 0»

$\frac{1}{2}mH_0^2{r^2} = \frac{4}{3}\pi G\rho {r^2}m$ ✔

«hence ρ_c= $\frac{{3H_0^2}}{{8\pi G}}$ »

Answer given, check working carefully.

Examiners report

This was a relatively easy demonstration given the equation in 22a. However many candidates did not show the process followed in a coherent manner that could be understood by examiners.

Syllabus sections

Option D: Astrophysics

Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics) » D.5 – Further cosmology (HL only)

Option D: Astrophysics » Option D: Astrophysics (Additional higher level option topics)

Question 19M.3.HL.TZ2.b

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