Download 中原大學 94 學年度轉學考招生入學考試

中原大學 94 學年度轉學考招生入學考試
7 月 19 日 14:00∼15:30 理工群組二年級
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科目： 普通物理
（共 4 頁第 1 頁）
þ可使用計算機，惟僅限不具可程式及多重記憶者
□不可使用計算機
所有的答案，請寫在答案卷上，若寫在試題上，不計分
一. 選擇題 (共 20 題，每題 2 分，計 40 分)
1. Let k be the Boltzmann constant. If the thermodynamic state of a gas at temperature T
changes isothermally(等溫的) and reversibly(可逆的) to a state with three times the
number of microstates as initially, the energy input to the gas as heat is:
(A) Q=0 (B) Q=3kT (C) Q=-3kT (D) kTln 3
2. In a certain gas the molecules are 5.0×10-9m apart on average, have a mean free path
of 5.0×10-6m, and have an average speed of 500 m/s. The rate at which a molecule has
collisions with other molecules is about: (A) 108 s-1 (B) 10-8 s-1 (C) 1 s-1 (D)1011 s-1
3. The same energy Q enters four different substances as heat.
(A) The temperature of 3 g of substance A increases by 10 K
(B) The temperature of 4 g of substance B increases by 4 K
(C) The temperature of 6 g of substance C increases by 15 K
(D) The temperature of 8 g of substance D increases by 6 K
Which substance has the greatest specific heat ?
4. A particle with a charge of 5×10-6 C and a mass of 20 g moves uniformly with a speed of
7 m/s in a circular orbit(圓形軌道)around a stationary(靜止的) particle with a charge of
-5×10-6 C. The radius of the orbit is: (A) 4.4 m (B) 0.23 m (C) 0.62 m (D) 1.6 m
5. The torque(力矩) exerted by an electric field on a dipole is:
(A) parallel to the field and perpendicular to the dipole moment
(B) parallel to the dipole moment and perpendicular to the field
(C) perpendicular to both the field and dipole moment
(D) not related to the directions of the field and dipole moment
6. A charged oil drop with a mass of 2×10-4 kg is held suspended(被懸浮) by a downward
electric field of 300 N/C. The charge on the drop is:
(A) +1.5 × 10-6 C (B) -1.5 × 10-6 C (C) +6.5 × 10-6 C (D) -6.5 × 10-6 C
7. 10 C of charge are placed on a spherical conducting shell. A particle with a charge of -3
C is placed at the center of the cavity(空洞). The net charge on the outer surface of the
shell is: (A) -7 C (B) -3 C (C) +7 C (D) +3 C
8. A 5-cm radius conducting sphere has a surface charge density of 2×10-6 C/m2 on its
surface. Its electric potential, relative to the potential far away, is:
(A) 1.1 × 104 V (B) 2.2×104 V (C) 2.3×105 V (D) 3.6×105 V
9. Two identical capacitors, each with capacitance C, are connected in parallel(並聯) and
the combination is connected in series(串聯) to a third identical capacitor. The
equivalent capacitance of this arrangement is: (A) 2C/3 (B) 3C (C) 3C/2 (D) 2C
10. An certain resistor dissipates(消耗) 0.5 W when connected to a 3 V potential difference.
When connected to a 1 V potential difference, this resistor will dissipate:
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(A) 0.5 W (B) 0.167 W (C) 1.5 W (D) 0.056 W
11. An electron is launched(發射) with velocity v in a uniform magnetic field B. The angle ?
between v and B is between 0° and 90°. As a result, the electron follows a helix(螺旋
線), its velocity vector v returning to its initial value in a time interval of:
(A) 2pmv sin?/eB (B) 2pmv/eB (C) 2p m/eB (D) 2pmv cos?/eB
12. Two long straight wires enter a room through a door. One carries a current of 3.0 A into
the room while the other carries a current of 5.0 A out. The magnitude of the path
integral ∮B．ds around the door frame is:
(A) 6.3 × 10-6 T．m (B) 3.8 × 10-6 T．m (C) 2.5 × 10-6 T．m (D) 1.0 × 10-5 T．m
13.“Beats”in sound refer to:
(A) interference of two waves of the same frequency
(B) combination of two waves of slightly different frequency
(C) two media(介質) having slightly different sound velocities
(D) effect of relative motion of source and observer
14. A string carries a sinusoidal wave with an amplitude(振幅) of 2.0 cm and a frequency of
100 Hz. The maximum speed of any point on the string is:
(A) 2.0 m/s (B) 4.0 m/s (C) 6.3 m/s (D) 13 m/s
15. A particle is in simple harmonic motion with period T. At time t=0 it is at the equilibrium
point. Of the following times, at which time is it furthest(最遠) from the equilibrium
point ？ (A) 0.5 T (B) 0.7 T (C) T (D) 1.4 T
16. One end of a cylindrical pipe(圓柱水管) has a radius of 1.5 cm. Water(density ＝ 1.0 ×
103 kg/m3) streams steadily out at 7.0 m/s. The rate at which mass is leaving the pipe
is: (A) 2.5 kg/s (B) 4.9 kg/s (C) 7.0 kg/s (D) 48 kg/s
17. The bulk modulus is a proportionality constant(比例常數) that relates the pressure
acting on an object to:
(A) the fractional change in volume (B) the fractional change in length
(C) Young's modulus (D) the spring constant
18. A hoop(圓環), a uniform disk, and a uniform sphere, all with the same mass and outer
radius, start with the same speed and roll without sliding up identical inclines(斜坡).
Rank the objects according to how high they go, least to greatest.
(A) hoop, disk, sphere (B) disk, hoop, sphere (C) sphere, hoop, disk
(D) sphere, disk, hoop
19. A wheel starts from rest and has an angular acceleration of 4.0 rad/s2. The time it takes
to make 10 rev is: (A) 0.50 s (B) 0.71 s (C) 5.6 s (D) 2.8 s
20. Whenever an object strikes a stationary(靜止的) object of equal mass:
(A) the collision must be elastic (B) the first object must stop
(C) momentum is not necessarily conserved (D) none of the above
二、填充題（每題3分，計60分）
1. Please give an example of an inertial reference frame.
__________________.
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2. Two blocks with masses m and M are pushed along a horizontal
ur
frictionless surface by a horizontal applied force F as shown. The magnitude
of the force that either of these blocks exerts on the other is ____________.
ur
F
M
m
3. Three identical objects, each of mass M , are fastened to a massless rod
of length L as shown. The rotational inertia about one end of the rod of this
array is _____________.
L/2
M
L/2
M
M
4. The potential energy for a 0.2-Kg particle that is acted on by a very massive
body and is moving along the x axis is given by U ( x ) = 8x 2 − 2 x 4 , where U
is in joules and x is in meters. When the particle is at x = 1.0 m its
acceleration is ____________.
5. Two identical disks, with rotational inertia I ( = 12 MR2 ) , roll without sliding
across a horizontal floor with the same speed and then up inclines. Disk A rolls
up its incline without sliding. On the other hand, disk B rolls up a frictionless
incline. Otherwise the inclines are identical. Disk A reaches a height 12cm
above the floor before rolling down again. Disk B reaches a height above the
floor of ____________ cm .
6. Suppose you have a pendulum clock that keeps correct time on Earth
(acceleration due to gravity = 9.8m / s 2 ). Without changing the clock, you take
it to the Moon (acceleration due to gravity = 1.6m / s 2 ). For every hour interval
(on Earth) the Moon clock will record ____________hour.
7. A Carnot refrigerator operates between a low temperature reservoir at Tc
and a high temperature reservoir at TH . Its coefficient of performance is
______________ (Express your answer in terms of Tc and TH ).
8. An ideal gas, consisting of n moles, undergoes a reversible isothermal
process during which the volume changes from Vi to
V f . The change in
entropy of the thermal reservoir in contact with the gas is
（共 4 頁第 4 頁）
____________(Express your answer in terms of n , Vi , and
V f ).
9. The unit of the electric field is ____________.
10. Positive charge Q is placed on a conducting spherical shell with inner
radius R1 and outer radius R2 . A point charge q is placed at the center of
the cavity. The magnitude of the electric field at a point inside the shell, a
distance r away from the center, is ____________.
11. Positive charge Q is placed on a conducting spherical shell with inner
radius R1 and outer radius R2 . A point charge q is placed at the center of
the cavity. The magnitude of the electric field at a point outside the shell, a
distance r away from the center, is ____________.
12. There is a parallel-plate capacitor in the circuit. The charges on each plate
are ± q , the plate area is A , and the separation between plates is d .
The capacitance of the capacitor is ____________.
13. Nine identical wires, each of diameter d and length L , are connected in
parallel. The combination has the same resistance as a single wire of length
L but whose diameter is ____________.
14. A proton (charge e ), traveling perpendicular to a magnetic field,
experiences the same force as an alpha particle (charge 2e ) which is also
traveling perpendicular to the same field. The ratio of their speeds, v proton / valpha ,
is ____________.
ur
r
15. The magnetic field at any point is given by B = Ar × k$ , where A is a
v
constant, r is the position vector of the point, and k$ is the unit vector along
the positive z -axis. The net current through a circle of radius R , in the
x − y plane and centered at the origin, is ____________ (Express your
answer in terms of A , R , and µ0 ).
16. A car travels northward at 75km / hour along a straight road in a region
where Earth's magnetic field has a vertical component of 0.5 × 10−4 T . The emf
induced between the left and right side, separated by 1.7m , is
____________.
17. An object of mass m , oscillating on the end of a spring with spring
constant k , has amplitude xm . Its maximum speed is ____________.
18. Give a physical quantity which has the same unit as the Planck constant h .
___________.
19. Give an evidence for the wave nature of matter. ________________.
20. Two events occur 100m apart with an intervening time interval of 0.37µ s .
The speed of a clock that measures the proper time between the events is
____________ (Express your answer in the unit of the speed of light c ).