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Question 19M.3.HL.TZ2.22b

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Date May 2019 Marks available [Maximum mark: 2] Reference code 19M.3.HL.TZ2.22b
Level HL Paper 3 Time zone TZ2
Command term Show that Question number b Adapted from N/A
b.
[Maximum mark: 2]
19M.3.HL.TZ2.22b

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.

(b)

At critical density there is zero total energy. Show that the critical density of the universe is:  r c = 3 H 0 2 8 π G .

[2]

Markscheme

substitutes H0r for v ✔

«total energy = 0»

1 2 m H 0 2 r 2 = 4 3 π G ρ r 2 m   ✔

«hence ρc = 3 H 0 2 8 π 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.

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