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Unformatted text preview: The University of Hong Kong
Department of Physics
First Semester Degree Examination (2008/2009) Basic Physics (PHYSI417) Date: December 18, 2008 Time Allowed: 1 hour Time: 2:30 pm. — 3:30 pm. Instructions to Candidates 0 Please put ALL answers on the answer book provided.
0 This examination paper has 6 pages and consists of two sections. 0 Section A: Multiple choices. Answer ALL questions. (48 marks) 0 Section B: Answer ALL questions (52 marks). 0 Useful data: Acceleration due to gravity g = 9.8 ms—2
Atmospheric pressure : 1.01 x 105 Pa
Universal gas constant R = 8.3145 Jmol_1K_1
Permittivity of free space so = 8.85x10‘12 C2 Nlm’z
Permeability of free space no = 1.26x10—6 TmA‘l Preﬁx: micro (u) = 10“, nano— (n) = 10‘9 Section A: Multiple Choice Questions (48 marks)
There are 12 questions in this section. Answer all of them. Write your answers in the answer book. 1. Block A, with mass mA, is initially at rest on a horizontal ﬂoor. Block B, with mass m3, is initially at rest on the horizontal top surface of A. The coefﬁcient of static friction between the two blocks is ,us. Block A is pulled with an increasing force. It begins to slide out from under B when its acceleration reaches A. g
B #35;
C. mgysg
D. (mA/mB)#sg
13 (ms/"10%?
2. A ladder leans against a wall. If the ladder is not to slip, which one of the following must be true? Wall
Ladder // Floor The coefﬁcient of friction between the ladder and the wall must not be zero The coefﬁcient of friction between the ladder and the ﬂoor must not be zero A
B
C. The ladder will not move down if it is heavy enough
D Both A and B E None of the above 3. Two uniform spheres X and Y are pivoted on horizontal axes that are tangent to their surfaces. The one with the longer period oscillation is the one with A. the larger mass B. the smaller mass C. the larger moment of inertia
D. the smaller moment of inertia
E. the larger radius In the formula F = Gm1m2/r2, the quantity G A. depends on the local value of g B. is used only when Earth is one of the two masses C. is greatest at the surface of Earth D. is a universal constant of nature E. is related to the Sun in the same way that g is related to Earth Each of the four corners of a square with edge a is occupied by a point mass m. There is a ﬁfth mass, also
m, at the center of the square. To remove the mass from the center to a point far away the work that must be done by an external agent is given by A. 4Gm2 /a B. —4Gm2 /a c. 4&sz /a
D. —4Gﬁm2 /a
E. 4sz /a2 A small satellite is in elliptical orbit around Earth as shown. If L denotes the magnitude of its angular momentum and K denotes kinetic energy: 2 1
A. L2>L1andK2>K1 L2>L1andK2=K1
C. L2=L1andK2=K1 L2=L1andK2>K1 E. L2=L1andK2<K1 Two rods have the same length at room temperature. The ﬁrst one is made of metal X while the second
one is made of metal Y and Z. The ratio of their linear expansivities (X : Y : Z) is 2 : l : 3. In order for the rods to have the same length at any temperature, what is the ratio of their respective lengths (11 : 12 : [3)? A. 2 : l :1
B. 3:1 :2
C. 3:2:1
D. 4:3 :1
E. Cannot be determined Any point on a string carrying a sinusoidal wave is moving with its maximum speed when A. the magnitude of its acceleration is a maximum B. the magnitude of its displacement is a maximum C. the magnitude of its displacement is a minimum D. the magnitude of its displacement is a half the amplitude E. the magnitude of its displacement is onefourth the amplitude Two ideal monatomic gases in thermal equilibrium with each other. Gas A is composed of molecules with mass m while gas B is composed of molecules with mass 4m. The ratio of the average molecular speeds vA/VB is A. 1/4
B. l/2
C. l
D. 2
E. 4 10. Point charges are located at two vertices of an equilateral triangle and the electric ﬁeld is zero at the third vertex. We conclude that A. the two charges have opposite signs and the same magnitude
B the two charges have opposite signs and different magnitudes
C the two charges are identical D. the two charges have the same signs but different magnitudes
E at least one other charge is present 11. A rectangular loop of wire ABCD is placed perpendicular to a uniform magnetic ﬁeld. It can rotate about an axis passing through the midpoints of AB and CD with frequency f. The induced emf is a maximum when
A. the ﬂux is zero
B the ﬂux is a maximum
C the ﬂux is half its maximum value
D. the derivative of the flux with respect to time is zero
E none of the above
12. An electron is launched with velocity 17 in a uniform magnetic ﬁeld E . The angle 6 between 17 and 1—53 is between 0 and 90°. As a result, the electron follows a helix, its velocity vector returning to its initial value in a time interval of A. 27zm/eB B (27071 sin6) / eB
C. 272mv /eB D (27zmvsin6l)/eB
E none of the above Section B (52 marks) There are ﬁve questions in this section. Answer all of them. 1. A uniform thin rod of length L and mass M is pivoted at one end. It is held horizontal and released under
the gravity. The moment of inertia of the rod about its end is ML2/3 and the gravitational acceleration is g.
Effect due to friction is negligible.
(3) Find the angular acceleration of the rod immediately after its release. (2 marks)
(b) Find the magnitude of the force exerted on the rod by the pivot at this instant. Please show the
direction of the force on a diagram. (8 marks) (c) Find the linear speed of the center of mass of the rod when it becomes vertical. (8 marks) (a)
(b) A bubble of 11 moles of helium is submerged at a certain depth in liquid water when the water and thus the
helium undergo a temperature increase of AT at constant pressure. As a result the bubble expands. The
helium is a monatomic ideal gas. As a reminder, detailed mathematical derivations are not required while
completing the following parts. Express your answers with n, AT and R, where R is the universal gas constant. Find the change in the internal energy of the helium during the temperature increase. (4 marks) Find the total energy that is added as heat to helium during the temperature increase and the expansion. (4 marks) A wedgeshaped film of air is made by placing a ﬁne fiber between the edges of two ﬂat pieces of glass.
Light of wavelength 500 nm is incident normally on the glass, and interference fringes are observed by
reﬂection. If the angle 9 made by the plates is 3.0 x 10‘4 radians, how many dark interference fringes per centimeter are observed? You may take the refractive index of air as l. (8 marks) Two particles execute simple harmonic motion of the same amplitude and frequency along close parallel
lines AB and A 'B’ respectively, where A, A’ and B, B’ are extreme points of the motions and each pair are very close points. The particles pass each other moving in opposite directions each time when their
displacement is half their amplitude. What is their phase difference? You answer should be within 0 and 71'. [Hint You may assume a particle performing simple harmonic motion has its displacement described by the equation: x = xm cos(a)t + ¢) , where x,,, is the amplitude of the oscillation, a) is the angular frequency and ¢ is the phase angle] (12 marks) A Ntum coil of radius r and resistance R sits in a region that has a uniform magnetic ﬁeld B normal to the plane of coil. Find the magnitude of the rate of change of the magnetic field to produce a current I in the coil? (6 marks) END OF PAPER ...
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 Spring '08
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 Mass, Moment Of Inertia

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