FUND.OF PHYSICS (LL)-PRINT COMP.VOL.2
12th Edition
ISBN: 9781119801269
Author: Halliday
Publisher: WILEY
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Textbook Question
Chapter 12, Problem 62P
A mine elevator is supported by a single steel cable 2.5 cm in diameter. The total mass of the elevator cage and occupants is 670 kg. By how much does the cable stretch when the elevator hangs by (a) 12 m of cable and (b) 362 m of cable? (Neglect the mass of the cable.)
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Question B3
Consider the following FLRW spacetime:
t2
ds² = -dt² +
(dx²
+ dy²+ dz²),
t2
where t is a constant.
a)
State whether this universe is spatially open, closed or flat.
[2 marks]
b) Determine the Hubble factor H(t), and represent it in a (roughly drawn) plot as a function
of time t, starting at t = 0.
[3 marks]
c) Taking galaxy A to be located at (x, y, z) = (0,0,0), determine the proper distance to galaxy
B located at (x, y, z) = (L, 0, 0). Determine the recessional velocity of galaxy B with respect
to galaxy A.
d) The Friedmann equations are
2
k
8πG
а
4πG
+
a²
(p+3p).
3
a
3
[5 marks]
Use these equations to determine the energy density p(t) and the pressure p(t) for the
FLRW spacetime specified at the top of the page.
[5 marks]
e) Given the result of question B3.d, state whether the FLRW universe in question is (i)
radiation-dominated, (ii) matter-dominated, (iii) cosmological-constant-dominated, or (iv)
none of the previous. Justify your answer.
f)
[5 marks]
A conformally…
SECTION B
Answer ONLY TWO questions in Section B
[Expect to use one single-sided A4 page for each Section-B sub question.]
Question B1
Consider the line element
where w is a constant.
ds²=-dt²+e2wt dx²,
a) Determine the components of the metric and of the inverse metric.
[2 marks]
b) Determine the Christoffel symbols. [See the Appendix of this document.]
[10 marks]
c)
Write down the geodesic equations.
[5 marks]
d) Show that e2wt it is a constant of geodesic motion.
[4 marks]
e)
Solve the geodesic equations for null geodesics.
[4 marks]
Chapter 12 Solutions
FUND.OF PHYSICS (LL)-PRINT COMP.VOL.2
Ch. 12 - A ladder leans against a frictionless wall but is...Ch. 12 - The table gives the initial lengths of three reds...Ch. 12 - An automobile with a mass of 1360 kg has 3.05 m...Ch. 12 - An archers bow is drawn at its midpoint until the...Ch. 12 - ILWA rope of negligible mass is stretched...Ch. 12 - A scaffold of mass 60 kg and Length 5.0 m is...Ch. 12 - A 75 kg window cleaner uses a 10 kg ladder that is...Ch. 12 - SSMA meter stick balances horizontally on a...Ch. 12 - A uniform cubical crate is 0.750 m on each side...Ch. 12 - A door has a height of 2.1 m along a y axis that...
Ch. 12 - SSM WWWA cubical box is filled with sand and...Ch. 12 - A crate, in the form of a cube with edge lengths...Ch. 12 - SSM ILWA horizontal aluminum rod 4.8 cm in...Ch. 12 - After a fall, a 95 kg rock climber finds himself...Ch. 12 - A uniform ladder whose length is 5.0 m and whose...Ch. 12 - A mine elevator is supported by a single steel...Ch. 12 - A solid copper cube has an edge length of 85.5 cm....Ch. 12 - A 73 kg man stands on a level bridge of length L....Ch. 12 - SSMA uniform cube of side length 8.0 cm rests cm a...Ch. 12 - A pan balance is made up of a rigid, massless rod...Ch. 12 - Prob. 76PCh. 12 - Prob. 77PCh. 12 - Prob. 78PCh. 12 - Prob. 79PCh. 12 - Prob. 80PCh. 12 - Prob. 81PCh. 12 - Prob. 82PCh. 12 - Prob. 83PCh. 12 - Prob. 84PCh. 12 - Prob. 85P
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