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Question 17N.3.HL.TZ0.b

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Date November 2017 Marks available [Maximum mark: 2] Reference code 17N.3.HL.TZ0.b
Level HL Paper 3 Time zone TZ0
Command term Calculate Question number b Adapted from N/A
b.
[Maximum mark: 2]
17N.3.HL.TZ0.b

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.

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

[2]

Markscheme

ALTERNATIVE 1 (10 ks is in observer frame):

Δt' =  10000 1 − 6.0 × 10 5 7.0 × 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 =  10000 1 − 6.0 × 10 5 7.0 × 10 8

10004 «ticks»

Allow ECF if 10 is used instead of 10000

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