DP Physics (last assessment 2024)

Test builder »

Question 18M.3.HL.TZ1.19

Select a Test
Date May 2018 Marks available [Maximum mark: 5] Reference code 18M.3.HL.TZ1.19
Level HL Paper 3 Time zone TZ1
Command term Draw, Explain, Show that Question number 19 Adapted from N/A
19.
[Maximum mark: 5]
18M.3.HL.TZ1.19

A galaxy can be modelled as a sphere of radius R0. The distance of a star from the centre of the galaxy is r.

M18/4/PHYSI/HP3/ENG/TZ1/19

For this model the graph is a simplified representation of the variation with r of the mass of visible matter enclosed inside r.

(a)

The mass of visible matter in the galaxy is M.

Show that for stars where r > R0 the velocity of orbit is v =  G M r .

[1]

Markscheme

m v 2 r = G M m r 2  and correct rearranging

[1 mark]

(b)

Draw on the axes the observed variation with r of the orbital speed v of stars in a galaxy.

[2]

Markscheme

linear / rising until R0 

then «almost» constant

[2 marks]

(c)

Explain, using the equation in (a) and the graphs, why the presence of visible matter alone cannot account for the velocity of stars when r > R0.

[2]

Markscheme

for v to stay constant for r greater than R0, M has to be proportional to r

 

but this contradicts the information from the M-r graph

OR

if M is constant for r greater than R0, then we would expect v ∝ r − 1 2

 

but this contradicts the information from the v-r graph

 

[2 marks]

Syllabus sections