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Date November 2017 Marks available 2 Reference code 17N.3.HL.TZ0.8
Level Higher level Paper Paper 3 Time zone Time zone 0
Command term Outline Question number 8 Adapted from N/A

Question

The Schwarzschild radius of a black hole is 6.0 x 105 m. A rocket is 7.0 x 108 m from the black hole and has a clock. The proper time interval between the ticks of the clock on the rocket is 1.0 s. These ticks are transmitted to a distant observer in a region free of gravitational fields.

Outline why the clock near the black hole runs slowly compared to a clock close to the distant observer.

[2]
a.

Calculate the number of ticks detected in 10 ks by the distant observer.

[2]
b.

Markscheme

this is gravitational time dilation

OR

black hole gives rise to a «strong» gravitational field

clocks in stronger field run more slowly

OR

the clock «signal» is subject to gravitational red-shift

the clock is subject to gravitational red shift

OR

the clock has lost gravitational potential energy in moving close to the black hole

[Max 2 Marks]

a.

ALTERNATIVE 1 (10 ks is in observer frame):

Δt' = \(10000\sqrt {1 - \frac{{6.0 \times {{10}^5}}}{{7.0 \times {{10}^8}}}} \)

9995.7 so 9995 «ticks»

Allow 9996

Allow ECF if 10 is used instead of 10000

ALTERNATIVE 2 (10 ks is in rocket frame):

Δt = \(\frac{{10000}}{{\sqrt {1 - \frac{{6.0 \times {{10}^5}}}{{7.0 \times {{10}^8}}}} }}\)

10004 «ticks»

Allow ECF if 10 is used instead of 10000

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.5 – General relativity (HL only)
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