Date | May 2012 | Marks available | 1 | Reference code | 12M.3.HL.TZ1.13 |
Level | Higher level | Paper | Paper 3 | Time zone | Time zone 1 |
Command term | State | Question number | 13 | Adapted from | N/A |
Question
This question is about the equivalence principle and black holes.
State the principle of equivalence.
The gravitational field strength near the surface of a neutron star is 1.2 ×1013Nkg–1. A light ray is emitted from a stationary probe at a height of 250 m above the surface. The frequency of the light measured in the probe is 4.8×1014 Hz.
(i) Determine the frequency of the light received at the surface of the star according to an observer at the surface.
(ii) Describe how gravitational red-shift leads to the concept of gravitational time dilation.
General relativity predicts the existence of black holes.
(i) State what is meant by a black hole.
(ii) Suggest two ways in which a black hole may be detected.
Markscheme
a frame of reference that is freely falling in a gravitational field is equivalent to an inertial frame of reference far from all masses;
or
inertial and gravitational effects are indistinguishable;
or
a frame of reference accelerating in empty space is equivalent to a frame of reference at rest in a gravitational field;
(i) \(\left( {\frac{{\Delta f}}{{{f_0}}} = \frac{{g\Delta h}}{{{c^2}}}{\rm{and so}}} \right)\Delta f = \left( {\frac{{1.2 \times {{10}^{13}} \times 250 \times 4.8 \times {{10}^{14}}}}{{9 \times {{10}^{16}}}} = } \right)0.16 \times {10^{14}}{\rm{Hz}}\);
\(f = \left( {4.8 \times {{10}^{14}} + 0.16 \times {{10}^{14}} = } \right)5.0 \times {10^{14}}{\rm{Hz}}\);
ECF applies only if the wrong value of Δf is added to f0.
(ii) as light travels away from a massive body it is red-shifted/frequency decreases/time period increases;
hence closer to the body the time period is shorter / time runs slower (than higher up) – this is (equivalent to) time dilation;
(i) a point of infinite curvature / a point of infinite space / a singularity of spacetime / a region from which nothing can escape / escape velocity ≥c;
(ii) matter falling into the black hole radiates;
the (gravitational) influence on other objects;
by observing its gravitational lensing effect;
emission of Hawking radiation;