英语数学选择题

1. At a certain time a moving particle ’s position vector is r , what is it speed?

A) dr dt B) dr dt C) d r dt D)

2. Which of the following is correct? A) , , d r dv v a dt dt ==B) , d v dr v a dt dt τ== C), ds dv v a dt dt

τ== D) , dr dv v a dt dt

==

3. Identical guns fire identical bullets horizontally at the same speed from the same

height above level planes, one on the Earth and one on the Moon. Which of the following three statements is/are true?

I. The horizontal distance traveled by the bullet is greater for the Moon. II. The flight time is less for the bullet on the Earth.

III. The velocity of the bullets at impact are the same.

A) III only B) I and II only C) I and III only D) II and III only

4. Two objects are traveling around different circular orbits with constant speed. They both have

the same acceleration but object A is traveling twice as fast as object B. The orbit radius for object A is _______ the orbit radius for object B.

A) one-fourth B) one-half C) the same as D) four times

5. The inertia of a body tends to cause the body to:

A) speed up B) slow down C) resist any change in its motion D) decelerate due to friction

6. 12. The "reaction" force does not cancel the "action" force because:

A) the action force is greater than the reaction force B) they act on different bodies

C) they are in the same direction D) the reaction force exists only after the action force is removed

7. Three identical springs (X,Y ,Z) are arranged as shown. When a

4.0-kg mass is hung on X, the mass descends 3.0 cm. When a

6.0-kg mass is hung on Y , the mass descends:

A) 2.0 cm

B) 4.0 cm

C) 6.0 cm

D) 9.0 cm

8. A 12-N horizontal force is applied to a 40-N block on a rough horizontal surface. The block

is initially at rest. If s μ= 0.5 and k μ= 0.4, the frictional force on the block is:

A) 8 N B) 12 N C) 16 N D) 20 N

9.When a certain rubber band is stretched a distance x, it exerts a restoring force F = ax + bx2,

where a and b are constants. The work done in stretching this rubber band from x = 0 to x = L is:

A) aL2 + bLx3B) aL + 2bL2C) a + 2bL D) aL2/2 + bL3/3

10.At time t = 0 a particle starts moving along the x axis. If its kinetic energy

increases uniformly with t the net force acting on it must be:

A) constant B) proportional to t D)

proportional to

11.An escalator is used to move 20 people (60 kg each) per

minute from the first floor of a department store to the

second floor, 5 m above. The power required is

approximately:

A) 100 W B) 200 W C) 1000 W D) 2000 W

12.Two objects interact with each other and with no other objects. Initially

object A has a speed of 5 m/s and object B has a speed of 10 m/s. In the

course of their motion they return to their initial positions. Then A has a

speed of 4 m/s and B has a speed of 7 m/s. We can conclude:

A) the potential energy changed from the beginning to the end of the trip.

B) mechanical energy was increased by nonconservative forces.

C) mechanical energy was decreased by nonconservative forces.

D) mechanical energy was increased by conservative forces.

13.The sum of the kinetic and potential energies of a system of objects is

conserved:

A) only when no external force acts on the objects.

B) only when the objects move along closed paths.

C) only when the work done by the resultant external force is zero.

D) none of the above.

14.A thick uniform wire is bent into the shape of the letter "U" as

shown. Which point indicates the location of the center of

mass of this wire?

A) A B) B C) C D) D

15.At one instant of time a rocket is traveling in outer space at

2500 m/s and is exhausting fuel at a rate of 100 kg/s. If the

speed of the fuel as it leaves the rocket is 1500 m/s, relative to

the rocket, the thrust is:

A) 0 B) 1.0 ×105 N C) 1.5 ×105 N D) 2.5 ×105 N

16.A He4nucleus (atomic weight 4) moving with speed v

breaks up into a neutron (atomic weight 1) and a He3

nucleus. The neutron moves off at right angles to the

original He4as shown. If the neutron speed is 3v, the

final speed of the He3 nucleus is:

A) zero B) v C) 4v/3 D) 5v/3

17.The angular velocity vector of a spinning body points out of the page. If the

angular acceleration vector points into the page then:

A) the body is slowing down

B) the body is speeding up

C) the body is starting to turn in the opposite direction

D) the axis of rotation is changing orientation

18.For a wheel spinning on an axis through its center, the ratio of the radial

acceleration of a point on the rim to the radial acceleration of a point halfway

between the center and the rim is:

A) 1/4 B) 2 C) 1/2 D) 4

19.Four identical particles, each with mass m, are arranged in the x, y plane

as shown. They are connected by light sticks to form a rigid body. If m =

2.0 kg and a = 1.0 m, the rotational inertia of this array about the y-axis

is:

A) 4.0 kg/m2 B) 12 kg/m2C) 9.6 kg/m2D) 4.8 kg/m2

20.A rod is pivoted about its center. A 5-N force is

applied 4 m from the pivot and another 5-N force is

applied 2 m from the pivot, as shown. The magnitude

of the total torque about the pivot (in N m) is:

0 B) 5 C) 8.7 D) 15

21.A man, with his arms at his sides, is spinning on a light frictionless turntable.

When he extends his arms:

A) his angular velocity increases.

B) his rotational inertia decreases.

C) his rotational kinetic energy increases.

D) his angular momentum remains the same.

22.A uniform disk has radius R and mass M. When it is spinning with angular

velocity w about an axis through its center and perpendicular to its face its angular momentum is Iw . When it is spinning with the same angle velocity about

a parallel axis a distance h away its angular momentum is:

A)(I -MR2)w B) (I + Mh2)w C) (I -Mh2)w D) (I + MR2)w

23.The escape velocity at the surface of Earth is approximately 8 km/s. What is the

escape velocity for a planet whose radius is 4 times and whose mass is 100 times that of Earth?

A) 1.6 km/s B) 8 km/s C) 40 km/s D) 200 km/s

24. In planetary motion the line from the star to the planet sweeps out equal areas in

equal times. This is a direct consequence of:

A) the conservation of energy B) the conservation of momentum

C) the conservation of angular momentum D) the conservation of mass

25. The amplitude of any oscillator can be doubled by:

A) doubling only the initial displacement B) doubling only the initial speed

C) doubling the initial displacement and halving the initial speed

D) doubling both the initial displacement and the initial speed

26. A certain spring elongates 9 mm when it is suspended vertically and a block of

mass M is hung on it. The natural frequency of this mass-spring system is:

A) need to know M B) 5.3 Hz C) 31.8 Hz D) 181.7 Hz

27. 40. A block attached to a spring undergoes simple harmonic motion on a

horizontal frictionless surface. Its total energy is 50 J. When the displacement is half the amplitude, the kinetic energy is:

A) 50 J B) 12.5 J C) 25 J D) 37.5 J

28. Both the x and y coordinates of a point execute simple harmonic motion. The

result might be a circular orbit if:

A) the amplitudes are the same but the frequencies are different

B) the amplitudes and frequencies are both the same

C) the amplitudes and frequencies are both different

D) the phase constants are the same but the amplitudes are different

29. The displacement of a string is given by ()(),sin m y x t y kx t ω=+. The wavelength of the wave is: A) 2πk /w B) k /w C) wk D) 2π/k

30. Suppose the maximum speed of a string carrying a sinusoidal wave is v s . When

the displacement of a point on the string is half its maximum, the speed of the point is:

A) 2s B) 2v s C) v s /4 D) 3v s /4

31. Two traveling sinusoidal waves interfere to produce a wave with the

mathematical form (,)sin()m y x t y kx t ωα=++. If the value of φ is appropriately chosen, the two waves might be:

A) 1(,) (/3)sin() m y x t y kx t ω=+and 2(,) (/3)sin( )m y x t y kx t ω?=++

B) 1(,) 0.7sin() m y x t y kx t ω=-and 2(,) 0.7sin( )m y x t y kx t ω?=-+

C) 1(,) 0.7sin() m y x t y kx t ω=+ and 2(,) 0.7sin( )m y x t y kx t ω?=++

D)

1(,) (/3)sin()

m

y x t y kx tω

=-and

2(,) (/3)sin( )

m

y x t y kx tω?

=++

32.When a certain string is clamped at both ends, the lowest four resonant

frequencies are 50, 100, 150, and 200 Hz. When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

A) 50, 100, 150, and 200 Hz

B) 50, 150, 250, and 300 Hz

C) 100, 200, 300, and 400 Hz

D) 25, 50 75, and 100 Hz

33.The diagram shows four situations in which a source of sound S and a detector D

are either moving or stationary. The arrows indicate the directions of motion. The speeds are all the same. Detector 3

is stationary. Rank the situations

according to the frequency

detected, lowest to highest.

A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 3, 4, 2 D) 2, 1, 2, 3

34.Heat is:

A) energy transferred by virtue of a temperature difference

B) energy transferred by macroscopic work

C) energy content of an object

D) a property objects have by virtue of their temperatures

35.According to the first law of thermodynamics, applied to a gas, the increase in the

internal energy during any process:

A) equals the heat input minus the work done on the gas

B) equals the heat input plus the work done on the gas

C) equals the work done on the gas minus the heat input

D) is independent of the heat input

36.According to the kinetic theory of gases, the pressure of a gas is due to:

A) change of kinetic energy of molecules as they strike the wall

B) change of momentum of molecules as the strike the wall

C) average kinetic energy of the molecules

D) force of repulsion between the molecules

37.The mass of an oxygen molecule is 16 times that of a hydrogen molecule. At

room temperature, the ratio of the rms speed of an oxygen molecule to that of a hydrogen molecule is:

A) 16 B) 4 C) 1/16 D) 1/4

38.The "Principle of Equipartition of Energy" states that the internal energy of a gas

is shared equally:

A) among the molecules

B) between kinetic and potential energy

C) among the relevant degrees of freedom

D) between translational and vibrational kinetic energy

39. The average speeds v and molecular diameters d of five ideal gases are given

below. The number of molecules per unit volume is the same for all of them. For which is the collision rate the greatest?

A) v = v 0 and d = d 0 B) v = 2v 0 and d = d 0/2

C) v = 3v 0 and d = d 0 D) v = v 0 and d = 2d 0

40. The mean free path of a gas molecule is:

A) average distance a molecule travels between intermolecular collisions

B) the cube root of the volume of the containing vessel

C) approximately the diameter of a molecule

D) average distance between adjacent molecules

41. In a reversible process the system:

A) is always close to equilibrium states

B) is close to equilibrium states only at the beginning and end

C) might never be close to any equilibrium state

D) is close to equilibrium states throughout, except at the beginning and end E) is none of the above

42. The difference in entropy B A S S S ?=- for two states A and B of a system can computed as the integral B

A dQ T ?provided:

A) A and B are on the same adiabat

B) A and B have the same temperature

C) a reversible path is used for the integral

D) the work done on the system is first computed

43. According to the second law of thermodynamics:

A) heat energy cannot be completely converted to work

B) work cannot be completely converted to heat energy

C) for all cyclic processes we have dQ/T < 0

D) the reason all heat engine efficiencies are less than 100% is friction, which is unavoidable

44. Choose the correct statement concerning electric field lines:

A) field lines may cross

B) field lines are close together where the field is large

C) field lines point away from negative charge

D) a point charge released from rest moves along a field line 45. Consider Gauss's law:0E dA q ε=?. Which of the following is true?

A)E must be the electric field due to the enclosed charge

B) If q = 0 then E = 0 everywhere on the Gaussian surface

C) If the charge inside consists of an electric dipole, then the integral is zero

D) If a charge is placed outside the surface, then it cannot affect E on the surface

46. Positive charge Q is distributed uniformly throughout an insulating sphere of

radius R , centered at the origin. A positive point charge Q is placed at x = 2R on the x axis. The magnitude of the electric field at x = R /2 on the x axis is:

A) ()20Q/4R πε B) ()20Q/8R πε C) ()20Q/72R πε D) ()2017Q/72R πε

47. A positive point charge Q is placed outside a large neutral conducting sheet. At

any point in the interior of the sheet the electric field produced by charges on the surface is directed:

A) toward the surface B) away from the surface C) toward Q D) away from Q

48. A hollow conductor is positively charged. A small uncharged metal ball is

lowered by a silk thread through a small opening in the top of the conductor and allowed to touch its inner surface. After the ball is removed, it will have:

A) a positive charge B) a negative charge C) no appreciable charge

D) a charge whose sign depends on what part of the inner surface it touched

49. A particle with mass m and, charge –q is projected with speed v 0 into

the region between two parallel plates as shown. The potential

difference between the two plates is V and their separation is d . The

change in kinetic energy of the particle as it traverses this region is:

A) –qV/d B) )2

02qV mv C) qV D) 202mv

50. Eight identical spherical raindrops are each at a potential V , relative to the

potential far away. They coalesce to make one spherical raindrop whose potential is:

A) 8V B ) V C) 2V D) 4V