College Physics
10th Edition
ISBN: 9781285737027
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Chapter 15, Problem 53P
Suppose the
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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 15 Solutions
College Physics
Ch. 15.1 - A suspended object A is attracted to a neutral...Ch. 15.2 - Object A has a charge of +2 C, and object B has a...Ch. 15.3 - A test charge of + 3 C is at a point P where the...Ch. 15.3 - A circular ring of charge of radius b has a total...Ch. 15.3 - A free electron and a free proton are placed in an...Ch. 15.4 - Rank the magnitudes of the electric field at...Ch. 15.8 - Calculate the magnitude of the flux of a constant...Ch. 15.8 - Suppose the electric field of Quick Quiz 15.7 is...Ch. 15.8 - Find the electric flux through the surface in...Ch. 15.8 - For a closed surface through which the net flux is...
Ch. 15 - A glass object receives a positive charge of +3 nC...Ch. 15 - The fundamental charge is e = 1.60 1019 C....Ch. 15 - Each of the following statements is related to...Ch. 15 - Two uncharged, conducting spheres are separated by...Ch. 15 - Four concentric spheres S1, S2, S3, and S4 are...Ch. 15 - IF a suspended object A is attracted to a charged...Ch. 15 - Positive charge Q is located at the center of a...Ch. 15 - Consider point A in Figure CQ15.8 located an...Ch. 15 - A student stands on a thick piece of insulating...Ch. 15 - In fair weather, there is an electric field at the...Ch. 15 - A charged comb often attracts small bits of dry...Ch. 15 - Why should a ground wire be connected to the metal...Ch. 15 - There are great similarities between electric and...Ch. 15 - A spherical surface surrounds a point charge q....Ch. 15 - If more electric field lines leave a Gaussian...Ch. 15 - A student who grew up in a tropical country and is...Ch. 15 - What happens when a charged insulator is placed...Ch. 15 - A 7.50-nC charge is located 1.80 m from a 4.20-nC...Ch. 15 - A charged particle A exerts a force of 2.62 N to...Ch. 15 - Rocket observations show that dust particles in...Ch. 15 - A small sphere of mass m = 7.50 g and charge q1 =...Ch. 15 - The nucleus of 8Be, which consists of 4 protons...Ch. 15 - A molecule of DNA (deoxyribonucleic acid) is 2.17...Ch. 15 - Two uncharged spheres are separated by 2.00 in. If...Ch. 15 - Four point charges are at the corners of a square...Ch. 15 - Two small identical conducting spheres are placed...Ch. 15 - Calculate the magnitude and direction of the...Ch. 15 - Three charges are arranged as shown in Figure...Ch. 15 - A positive charge q1 = 2.70 C on a frictionless...Ch. 15 - Three point charges are located at the corners of...Ch. 15 - Two identical metal blocks resting on a...Ch. 15 - Two small metallic spheres, each of mass m = 0.20...Ch. 15 - Panicle A of charge 3.00 104 C is at the origin,...Ch. 15 - A small object of mass 3.80 g and charge 18.0 C is...Ch. 15 - (a) Determine the electric field strength at a...Ch. 15 - An electric field of magnitude 5.25 105 N/C...Ch. 15 - An electron is accelerated by a constant electric...Ch. 15 - Charge q1 = 1.00 nC is at x1 = 0 and charge q2 =...Ch. 15 - A small sphere of charge q = +68 C and mass m =...Ch. 15 - A proton accelerates from rest in a uniform...Ch. 15 - (a) Find the magnitude and direction of the...Ch. 15 - Four point charges are located at the corners of a...Ch. 15 - A helium nucleus of mass m = 6.64 1027 kg and...Ch. 15 - A charged dust particle at rest in a vacuum is...Ch. 15 - A particle of mass 1.00 109 kg and charge 3.00 pC...Ch. 15 - Two equal positive charges are at opposite corners...Ch. 15 - Three point charges are located on a circular are...Ch. 15 - In Figure P15.31, determine the point (other than...Ch. 15 - Three charges are at the corners of an equilateral...Ch. 15 - Three identical charges (q = 5.0 C.) lie along a...Ch. 15 - Figure P15.31 shows the electric held lines for...Ch. 15 - (a) Sketch the electric field lines around an...Ch. 15 - (a) Sketch the electric field pattern around two...Ch. 15 - Two point charges are a small distance apart. (a)...Ch. 15 - Three equal positive charges are at the corners of...Ch. 15 - Refer 10 Figure 15.20. The charge lowered into the...Ch. 15 - The dome of a Van de Graaff generator receives a...Ch. 15 - If the electric field strength in air exceeds 3.0 ...Ch. 15 - In the Millikan oil-drop experiment illustrated in...Ch. 15 - A Van de Graaff generator is charged so that a...Ch. 15 - A uniform electric field of magnitude E = 435 N/C...Ch. 15 - An electric field of intensity 3.50 kN/C is...Ch. 15 - The electric field everywhere on the surface of a...Ch. 15 - Four closed surfaces, S1 through S4, together with...Ch. 15 - A charge q = +5.80 C is located at the center of a...Ch. 15 - Figure P15.49 shows a closed cylinder with...Ch. 15 - A charge of q = 2.00 109 G is spread evenly on a...Ch. 15 - A point charge q is located at the center of a...Ch. 15 - A charge of 1.70 102 C is at the center of a cube...Ch. 15 - Suppose the conducting spherical shell of Figure...Ch. 15 - A very large nonconducting plate lying in the...Ch. 15 - In deep spare, two spheres each of radius 5.00 m...Ch. 15 - A nonconducting, thin plane sheet of charge...Ch. 15 - Three point charges are aligned along the x-axis...Ch. 15 - A small plastic ball of mass m = 2.00 g is...Ch. 15 - A proton moving at v0 = 1.50 106 m/s enters the...Ch. 15 - The electrons in a particle beam each have a...Ch. 15 - A point charge +2Q is at the origin and a point...Ch. 15 - A 1.00-g cork ball having a positive charge of...Ch. 15 - Two 2.0-g spheres are suspended by 10.0-cm-long...Ch. 15 - a point charge of magnitude 5.00 C is at the...Ch. 15 - Two hard rubber spheres, each of mass m = 15.0 g,...Ch. 15 - Prob. 66APCh. 15 - A solid conducting sphere of radius 2.00 cm has a...Ch. 15 - Three identical point charges, each of mass m =...Ch. 15 - Each of the electrons in a particle beam has a...Ch. 15 - Protons are projected with an initial speed v0 = 9...
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