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Question 18M.3.HL.TZ2.7

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Date May 2018 Marks available [Maximum mark: 5] Reference code 18M.3.HL.TZ2.7
Level HL Paper 3 Time zone TZ2
Command term Calculate, Discuss, Outline Question number 7 Adapted from N/A
7.
[Maximum mark: 5]
18M.3.HL.TZ2.7

It is believed that a non-rotating supermassive black hole is likely to exist near the centre of our galaxy. This black hole has a mass equivalent to 3.6 million times that of the Sun.

(a.i)

Outline what is meant by the event horizon of a black hole.

[1]

Markscheme

boundary inside which events cannot be communicated to an outside observer

OR

distance/surface at which escape velocity = c

 

OWTTE

[1 mark]

(a.ii)

Calculate the distance of the event horizon of the black hole from its centre.

                                                                   Mass of Sun = 2 × 1030 kg

[2]

Markscheme

mass of black hole = 7.2 × 1036 «kg»

« 2 G M c 2 =» 1 × 1010 «m»

 

[2 marks]

(b)

Star S-2 is in an elliptical orbit around a black hole. The distance of S-2 from the centre of the black hole varies between a few light-hours and several light-days. A periodic event on S-2 occurs every 5.0 s.

M18/4/PHYSI/HP3/ENG/TZ2/07.b

Discuss how the time for the periodic event as measured by an observer on the Earth changes with the orbital position of S-2.

[2]

Markscheme

wherever S-2 is in orbit, time observed is longer than 5.0 s

when closest to the star S-2 periodic time dilated more than when at greatest distance

Justification using formula or time is more dilated in stronger gravitational fields

 

[2 marks]

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