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

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

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.

(a)

Justify that the total energy of this particle is E = 1 2 m v 2 − 4 3 π G r r 2 m .

[2]

Markscheme

total energy=kinetic energy+potential energy

OR

total energy= 1 2 m v 2 − G M m r ✔

substitution of M = 4 3 π r 3 ρ ✔

«Hence answer given»

Answer given so for MP2 look for clear evidence that MUniverse ( 4 3 π r 3 ρ ) is stated and substituted.

Examiners report

The vast majority of the candidates could state that the total energy is equal to the sum of the kinetic and potential energies but quite a few did not use the correct formula for the gravitational potential energy. The formula for the mass of the sun was usually correctly substituted.

Syllabus sections