Physics for Scientists and Engineers
9th Edition
ISBN: 9781133947271
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 34, Problem 34.1OQ
A spherical interplanetary grain of dust of radius 0.2 μm is at a distance r1 from the Sun. The gravitational force exerted by the Sun on the grain just balances the force due to
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ROTATIONAL DYNAMICS
Question 01
A solid circular cylinder and a solid spherical ball of the same mass and radius are rolling
together down the same inclined. Calculate the ratio of their kinetic energy. Assume pure
rolling motion Question 02
A sphere and cylinder of the same mass and radius start from ret at the same point and more
down the same plane inclined at 30° to the horizontal
Which body gets the bottom first and what is its acceleration
b) What angle of inclination of the plane is needed to give the slower body the same
acceleration
Question 03
i)
Define the angular velocity of a rotating body and give its SI unit
A car wheel has its angular velocity changing from 2rads to 30 rads
seconds. If the radius of the wheel is 400mm. calculate
ii)
The angular acceleration
iii)
The tangential linear acceleration of a point on the rim of the wheel
Question 04
in 20
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 34 Solutions
Physics for Scientists and Engineers
Ch. 34 - Prob. 34.1QQCh. 34 - What is the phase difference between the...Ch. 34 - Prob. 34.3QQCh. 34 - Prob. 34.4QQCh. 34 - If the antenna in Figure 33.11 represents the...Ch. 34 - Prob. 34.6QQCh. 34 - A radio wave of frequency on the order of 105 Hz...Ch. 34 - A spherical interplanetary grain of dust of radius...Ch. 34 - Prob. 34.2OQCh. 34 - A typical microwave oven operates at a frequency...
Ch. 34 - Prob. 34.4OQCh. 34 - Prob. 34.5OQCh. 34 - Which of the following statements are true...Ch. 34 - Prob. 34.7OQCh. 34 - Prob. 34.8OQCh. 34 - An electromagnetic wave with a peak magnetic field...Ch. 34 - Prob. 34.10OQCh. 34 - Prob. 34.11OQCh. 34 - suppose a creature from another planet has eyes...Ch. 34 - Prob. 34.2CQCh. 34 - Prob. 34.3CQCh. 34 - List at least three differences between sound...Ch. 34 - If a high-frequency current exists in a solenoid...Ch. 34 - Prob. 34.6CQCh. 34 - Prob. 34.7CQCh. 34 - Do Maxwells equations allow for the existence of...Ch. 34 - Prob. 34.9CQCh. 34 - What does a radio wave do to the charges in the...Ch. 34 - Prob. 34.11CQCh. 34 - An empty plastic or glass dish being removed from...Ch. 34 - Prob. 34.13CQCh. 34 - Prob. 34.1PCh. 34 - Prob. 34.2PCh. 34 - Prob. 34.3PCh. 34 - An election moves through a uniform electric field...Ch. 34 - A proton moves through a region containing a...Ch. 34 - Prob. 34.6PCh. 34 - Suppose you are located 180 in from a radio...Ch. 34 - A diathermy machine, used in physiotherapy,...Ch. 34 - The distance to the North Star, Polaris, is...Ch. 34 - Prob. 34.10PCh. 34 - Review. A standing-wave pattern is set up by radio...Ch. 34 - Prob. 34.12PCh. 34 - The speed of an electromagnetic wave traveling in...Ch. 34 - A radar pulse returns to the transmitterreceiver...Ch. 34 - Figure P34.15 shows a plane electromagnetic...Ch. 34 - Verify by substitution that the following...Ch. 34 - Review. A microwave oven is powered by a...Ch. 34 - Why is the following situation impossible? An...Ch. 34 - ln SI units, the electric field in an...Ch. 34 - At what distance from the Sun is the intensity of...Ch. 34 - If the intensity of sunlight at the Earths surface...Ch. 34 - Prob. 34.22PCh. 34 - A community plans to build a facility to convert...Ch. 34 - Prob. 34.24PCh. 34 - Prob. 34.25PCh. 34 - Review. Model the electromagnetic wave in a...Ch. 34 - High-power lasers in factories are used to cut...Ch. 34 - Consider a bright star in our night sky. Assume...Ch. 34 - What is the average magnitude of the Poynting...Ch. 34 - Prob. 34.30PCh. 34 - Review. An AM radio station broadcasts...Ch. 34 - Prob. 34.32PCh. 34 - Prob. 34.33PCh. 34 - Prob. 34.34PCh. 34 - A 25.0-mW laser beam of diameter 2.00 mm is...Ch. 34 - A radio wave transmits 25.0 W/m2 of power per unit...Ch. 34 - Prob. 34.37PCh. 34 - Prob. 34.38PCh. 34 - A uniform circular disk of mass m = 24.0 g and...Ch. 34 - The intensity of sunlight at the Earths distance...Ch. 34 - Prob. 34.41PCh. 34 - Assume the intensity of solar radiation incident...Ch. 34 - A possible means of space flight is to place a...Ch. 34 - Extremely low-frequency (ELF) waves that can...Ch. 34 - A Marconi antenna, used by most AM radio stations,...Ch. 34 - A large, flat sheet carries a uniformly...Ch. 34 - Prob. 34.47PCh. 34 - Prob. 34.48PCh. 34 - Two vertical radio-transmitting antennas are...Ch. 34 - Prob. 34.50PCh. 34 - What are the wavelengths of electromagnetic waves...Ch. 34 - An important news announcement is transmitted by...Ch. 34 - In addition to cable and satellite broadcasts,...Ch. 34 - Classify waves with frequencies of 2 Hz, 2 kHz, 2...Ch. 34 - Assume the intensity of solar radiation incident...Ch. 34 - In 1965, Arno Penzias and Robert Wilson discovered...Ch. 34 - The eye is most sensitive to light having a...Ch. 34 - Prob. 34.58APCh. 34 - One goal of the Russian space program is to...Ch. 34 - A microwave source produces pulses of 20.0GHz...Ch. 34 - The intensity of solar radiation at the top of the...Ch. 34 - Prob. 34.62APCh. 34 - Consider a small, spherical particle of radius r...Ch. 34 - Consider a small, spherical particle of radius r...Ch. 34 - A dish antenna having a diameter of 20.0 m...Ch. 34 - The Earth reflects approximately 38.0% of the...Ch. 34 - Review. A 1.00-m-diameter circular mirror focuses...Ch. 34 - Prob. 34.68APCh. 34 - Prob. 34.69APCh. 34 - You may wish to review Sections 16.4 and 16.8 on...Ch. 34 - Prob. 34.71APCh. 34 - Prob. 34.72APCh. 34 - Prob. 34.73APCh. 34 - Prob. 34.74APCh. 34 - Prob. 34.75APCh. 34 - Prob. 34.76CPCh. 34 - A linearly polarized microwave of wavelength 1.50...Ch. 34 - Prob. 34.78CPCh. 34 - Prob. 34.79CP
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