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Principles of Physics is an introductory course designed to provide a comprehensive foundation in the fundamental concepts and laws that govern the physical world. Topics include mechanics, motion, energy, thermodynamics, waves, electricity, magnetism, and optics. Learning emphasizes the quantitative and qualitative understanding of the physical phenomena through theoretical explanations, problem-solving, and real-world applications. The course integrates experimental demonstrations and laboratory work to enhance conceptual grasp and develop analytical skills necessary for advanced studies in science and engineering.
Recommended Textbook
Physics 4th Edition by James S. Walker
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Q1) How long does it take for a train traveling 60.4 miles per hour to travel 81 miles?
A) 0.75 hours
B) 0.745 hours
C) 1.34 hours
D) 1.3 hours
E) 1 hour
Answer: D
Q2) If you are measuring the length of a room, the most appropriate SI unit is the A) kilometer.
B) meter.
C) centimeter.
D) millimeter.
E) micrometer.
Answer: B
Q3) What are the dimensions of volume?
Answer: [L<sup>3</sup>]
Q4) What are the dimensions of area?
Answer: [L<sup>2</sup>]
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Q1) The area under a curve in a velocity versus time graph gives A) distance traveled.
B) displacement.
C) speed.
D) velocity.
E) acceleration.
Answer: B
Q2) Car A is traveling at twice the speed of car B. They both hit the brakes at the same time and undergo identical decelerations. How does the distance required for car A to stop compare with that for car B?
Answer: It takes four times the distance to stop.
Q3) A certain car can accelerate from 0 to 100 km/hr in 6.0 seconds. What is the average acceleration of that car in m/s<sup>2</sup>?
Answer: 4.6 m/s<sup>2</sup>
Q4) An object thrown upward experiences free fall.
A)True
B)False
Answer: True
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Q1) A car travels along eastward with a constant velocity. The magnitude of the acceleration of the car is
A) decreasing.
B) increasing.
C) non-zero constant.
D) zero.
E) None of the other choices is correct.
Answer: D
Q2) A vector with zero magnitude can have one or more components that are nonzero.
A)True
B)False
Answer: False
Q3) The sum of two vectors has the greatest magnitude when the angle between these two vectors is
A) 90°.
B) 180°.
C) 60°.
D) 0°.
E) 270°.
Answer: D
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Q1) A monkey is sitting at the top of a tree 20 m high from the ground level. A person standing on the ground wants to feed the monkey. He uses a bow and arrow to launch the food to the monkey. If the monkey remains seated at the top of the tree, how should the person aim the arrow containing the food so that the monkey gets the food?
A) He should aim it at the monkey.
B) He should aim it below the monkey.
C) He should aim it above the monkey.
D) None of the other choices is correct.
Q2) The horizontal and vertical components of the initial velocity of a football are 24 m/s and 7 m/s respectively. What is the initial velocity of the football?
A) 31 m/s
B) 25 m/s
C) 17 m/s
D) 42 m/s
E) 625 m/s
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Q1) Mass is a measure of how difficult it is to change the velocity of an object.
A)True
B)False
Q2) A 10.0-kg picture is held in place by two wires, one hanging at 50.0° to the left of the vertical and the other at 45.0° to the right of the vertical. What is the tension in the second wire?
A) 71.8 N
B) 75.4 N
C) 98.1 N
D) 69.4 N
E) 23.8 N
Q3) The mass of an object is fixed, but its weight varies from location to location.
A)True
B)False
Q4) A force is required for an object to move.
A)True B)False
Q5) A 45-kg person steps on a scale in an elevator. The scale reads 460 N. What is the elevator doing?
Q6) State Newton's second law of motion.
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Q1) An airplane is flying with constant speed along a horizontal circle. Is the direction of its acceleration constant?
Q2) The force fo static friction between two surfaces is parallel to the surface of contact, and in in the direction that opposes relative motion.
A)True B)False
Q3) Refer to Figure 6-13. Block A has a mass of 5.00 kg, block B has a mass of 3.00 kg and block C has a mass of 2.00 kg. The pulleys are ideal and there is no friction between block B and the table. What is the tension in the string connecting blocks A and B?
A) 13.7 N
B) 20.6 N
C) 34.3 N
D) 25.5 N
E) 38.3 N
Q4) Why does a cyclist tilt her bicycle on a curve?
Q5) A net horizontal force is required for a body to move in a horizontal circle.
A)True B)False
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Q1) If the work done to stretch a spring by 4.0 cm is 6.0 J, what is the spring constant?
A) 300 N/m
B) 3000 N/m
C) 3500 N/m
D) 7500 N/m
E) 6000 N/m
Q2) What is the horsepower needed to change the speed of a 1600-kg sport utility vehicle from 15.0 m/s to 40.0 m/s in 4.00 seconds?
A) 369 hp
B) 36.9 hp
C) 18.8 hp
D) 188 hp
E) 275 hp
Q3) If the net work done on an object is zero, then the object's kinetic energy
A) decreases.
B) remains the same.
C) increases.
D) is zero.
E) cannot be determined without knowing the object mass.
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Q1) You need to load a crate of mass m onto the bed of a truck. One possibility is to lift the crate straight up over a height h, equal to height of the truck's bed. The work done in this case is W<sub>1</sub>. The other possibility is to slide the crate up the frictionless ramp of length L as shown in Figure 8-1. In this case you perform work W<sub>2</sub>.
What statement is true?
A) W<sub>1</sub> < W<sub>2</sub>
B) W<sub>1</sub> = W<sub>2</sub>
C) W<sub>1</sub> > W<sub>2</sub>
D) No simple relationship exists between W<sub>1</sub> and W<sub>2</sub>.
Q2) A ball drops some distance and gains 30 J of kinetic energy. Do not ignore air resistance. How much gravitational potential energy did the ball lose?
A) more than 30 J
B) exactly 30 J
C) less than 30 J
D) Cannot be determined from the information given.
Q3) What distinguishes a conservative force from a non-conservative force?
Q4) The frictional force is a conservative force.
A)True
B)False
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Q1) A rubber ball and a lump of putty have equal mass. They are thrown with equal speed against a wall. The ball bounces back with nearly the same speed with which it hit. The putty sticks to the wall. Which objects experiences the greater momentum change?
A) the ball
B) the putty
C) Both experience the same non-zero momentum change.
D) Both experience zero momentum change.
E) Cannot be determined from the information given.
Q2) A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 200-g piece moves along the x-axis with a speed of 2.00 m/s, a 235-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. What is its speed?
A) 2.51 m/s
B) 2.57 m/s
C) 3.50 m/s
D) 5.33 m/s
E) 6.83 m/s
Q3) State the Conservation of Linear Momentum.
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Q1) Figure 10-2 illustrates a simplified roller bearing. The outer hollow cylinder has a radius of 1.2 cm and is stationary. The inner cylinder has a radius of 1.0 cm and is rotating at 10 rpm. Between the two cylinders are several small cylinders with a radius of 0.10 cm, which roll without slipping on both the inner and outer cylinders. Only one of these cylinders is shown in the figure. What is the angular speed of the small cylinders?
A) 12 rpm
B) 10 rpm
C) 20 rpm
D) 62 rpm
E) 50 rpm
Q2) When a rigid body rotates about a fixed axis all the points in the body have the same angular displacement.
A)True
B)False
Q3) The Sun subtends an angle of 0.00928 radians at the surface of the earth. Its distance from Earth is 1.50 x 10<sup>11 </sup>m. What is the diameter of the Sun?
Q4) Express an angle of 450° in radians.
Q5) What is the angular speed in rad/s of the minute hand of a clock?
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Q1) The wheelbase on a 50,000-kg truck is 2.40 m wide and the truck's center of mass is located along the vertical centerline of the truck and 2.00 m above the bottom of the tires. The truck is going around a horizontal turn with a radius of 180 m. What is the maximum speed at which the truck can go around the curve without some of its tires lifting off the road?
A) 44.3 m/s
B) 38.2 m/s
C) 32.5 m/s
D) 28.2 m/s
E) 25.0 m/s
Q2) You are holding on to the axle of a spinning bicycle wheel with one hand on either side of the wheel. The top part of the wheel is moving away from you and the bottom is moving toward you and the axle is horizontal. In what direction do you need to apply a torque for the wheel to turn to the left?
A) toward you
B) away from you
C) vertically up
D) vertically down
E) to your right
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Q1) The gravitational force between two objects is proportional to
A) the distance between the two objects.
B) the square of the distance between the two objects.
C) the product of the masses of the two objects.
D) the square of the product of the masses of the two objects.
E) none of the above
Q2) Kepler's second law tells us that planets sweep out equal areas in equal times. If you compare the amount of area per time swept by Earth with the one of Jupiter, you would conclude:
A) They sweep the same area per time.
B) They sweep different areas per time.
C) Jupiter sweeps a larger area per time because it has much more mass than Earth.
D) Earth sweeps a larger area per time because it has much less mass than Jupiter.
Q3) State Kepler's Third Law of Orbital Motion
Q4) Tides are approximately 24 hours apart.
A)True
B)False
Q5) State Kepler's Second Law of Orbital Motion
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Q1) The total mechanical energy of a simple harmonic oscillator is
A) zero as it passes the equilibrium point.
B) zero when it reaches the maximum displacement.
C) a maximum when it passes through the equilibrium point.
D) a minimum when it passes through the equilibrium point.
E) constant.
Q2) A 4.20-g bullet embeds itself in a 20.0-kg block, which is attached to a horizontal spring with a force constant of 950 N/m. The maximum compression of the spring is 2.10 cm. What is the speed of the bullet just before it hits the block?
A) 690 m/s
B) 700 m/s
C) 672 m/s
D) 900 m/s
E) 952 m/s
Q3) A child and an adult are walking. Their legs swing like physical pendulums and both swing through the same maximum angle. The adult is 1.5 times as tall as the child, and all their dimensions are scaled proportionately. They also have the same mass per unit volume. How many steps does the child take in the time that the adult takes 49 steps?
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Q1) In the open ocean, the tides are waves that have a period of 12 hours and a speed of 750 km/hr. What is their wavelength?
Q2) As you stand by the side of the road, a car approaches you at a constant speed, sounding its horn, and you hear a frequency of 76 Hz. After the car goes by, you hear a frequency of 65 Hz. What is the speed of the car? The speed of sound in air is 343 m/s.
A) 26 m/s
B) 27 m/s
C) 28 m/s
D) 29 m/s
E) 30 m/s
Q3) A car horn emits a frequency of 400 Hz. A car traveling at 20.0 m/s sounds the horn as it goes away from a stationary pedestrian. What frequency does the pedestrian hear? The speed of sound in air is 343 m/s.
A) 378 Hz
B) 389 Hz
C) 411 Hz
D) 422 Hz
E) 450 Hz
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Q1) A spar buoy consists of a circular cylinder, which floats with its axis oriented vertically. One such buoy has a radius of 1.00 m, a height of 2.00 m, and weighs 40.0 kN. What portion of it is submerged when it is floating in fresh water?
A) 1.35 m
B) 1.30 m
C) 1.25 m
D) 1.20 m
E) 1.50 m
Q2) A 1959 penny has a diameter of 19.55 mm, a thickness of 1.55 mm, and a mass of 2.500 g. What is its density?
A) 5.37 × 10<sup>3</sup> kg/m<sup>3</sup>
B) 21.5 × 10<sup>3</sup> kg/m<sup>3</sup>
C) 1.34 × 10<sup>3</sup> kg/m<sup>3</sup>
D) 2.68 × 10<sup>3</sup> kg/m<sup>3</sup>
E) 1.86 × 10<sup>-4</sup> kg/m<sup>3</sup>
Q3) State Pascal's Principle
Q4) Does atmospheric pressure affect the buoyant force on a rigid submarine? Explain why or why not.
Q5) State Archimedes' Principle.
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Q1) The type of heat transfer that occurs between a stove and a pot placed on it is
A) convective.
B) conductive.
C) radiative.
D) countercurrent.
E) evaporation.
Q2) At what rate is the human body radiating energy when it is at 33°C? Take the body surface area to be 1.4 m<sup>2</sup>, and approximate the body as a black body.
Q3) The amount of heat that flows through a rod whose ends are held at different temperatures is proportional to the length of the rod.
A)True
B)False
Q4) The thermal conductivity of concrete is 0.80 W/m-C° and the thermal conductivity of wood is 0.10 W/m-C°. How thick would a solid concrete wall have to be in order to have the same rate of flow through it as an 8.0 cm thick wall made of solid wood? (Assume both walls have the same surface area.)
Q5) Does it make sense to say that an object has twice as much heat as another? Why?
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Q1) How much heat must be removed from 456 g of water at 25.0°C to change it into ice at -10.0°C?
The specific heat of ice is 2090 J/(kg K) and the latent heat of fusion of water is 33)5 × 10<sup>4</sup> J/kg.
A) 105 kJ
B) 153 kJ
C) 57.3 kJ
D) 47.7 kJ
E) 210 kJ
Q2) The internal energy of an ideal gas depends on
A) its pressure.
B) its volume.
C) its temperature.
D) its temperature and pressure.
E) its temperature, pressure, and volume.
Q3) What is the rms speed of a helium atom:
(a) at 5. K?
(b) at -196.° C (the boiling point of N<sub>2</sub>)?
(c) at 100.° C?
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Q1) A certain ideal gas has a molar specific heat at constant volume C<sub>v</sub> = 7R/5. What is its molar specific heat at constant pressure?
A) 12R/5
B) 7R/3
C) 12R/7
D) 12R/5.
E) 4R
Q2) 1.50 moles of an ideal monatomic gas are initially at a temperature of 317 K. If the gas gains 2730 J of heat and performs 780 J of work, what is its final temperature?
A) 359 K
B) 421 K
C) 526 K
D) 687 K
E) 756 K
Q3) A Diesel engine uses adiabatic heating to ignite the fuel.
A)True
B)False
Q4) State the First Law of Thermodynamics.
Q5) State the Zeroth Law of Thermodynamics.
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Q1) An electron is placed in a constant electric field of 4.5 × 10<sup>4</sup> N/C.
(a) What is the force on the electron?
(b) If the electron is released from rest, what is its speed after 3.0 ps?
Q2) Q<sub>1</sub> = 6.0 nC is at (0.30 m, 0); Q<sub>2</sub> = -1.0 nC is at (0, 0.10 m); Q<sub>3</sub> = 5.0 nC is at (0, 0). What is the magnitude and direction of the net force on the 5.0 nC charge?
Q3) A point charge Q = 7.00 × 10<sup>-9</sup> C is placed at the origin of an xy-coordinate system. What is the electric field intensity E at a distance of x = 30 cm from this charge? (Use k = 9 × 10<sup>9</sup> Nm<sup>2</sup>/C<sup>2</sup>.)
A) 100 N/C
B) 400 N/C
C) 500 N/C
D) 600 N/C
E) 700 N/C
Q4) An electrically neutral atom does not have a net charge.
A)True
B)False
Q5) A metal sphere of radius 2.0 cm carries a charge of 3.0 C. What is the electric field 6.0 cm from the center of the sphere?
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Q1) The potential energy at x = 8 m is -2000 V and at x = 2 m is +400 V. What is the magnitude and direction of the electric field?
A) 200 V/m directed parallel to the +x-axis
B) 300 V/m directed parallel to the +x-axis
C) 400 V/m directed parallel to the +x-axis
D) 500 V/m directed parallel to the +x-axis
E) 600 V/m directed parallel to the +x-axis
Q2) Two point charges of magnitude +4.00 C and +2.00 C are placed at the opposite corners of a rectangle as shown in Figure 20-10. What is the potential at point B due to these two charges?
A) 1.13 × 10<sup>3</sup> V
B) 11.3 × 10<sup>3</sup> V
C) -11.3 × 10<sup>3</sup> V
D) -113 × 10<sup>3</sup> V
E) 113 × 10<sup>3</sup> V
Q3) After being charged from a battery, the plates of a parallel plate capacitor are moved closer together. When they are half as far apart as originally, by how much does the stored energy change?
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Q1) A light bulb operating at a voltage of 120 Volt has a power of 60 W. What is the current flowing through this bulb?
A) 1.5 A
B) 2.5 A
C) 0.5 A
D) 2 A
E) 1 A
Q2) Four capacitors are connected across a 90-V DC source as shown in Figure 21-19. What is the charge on the 4.0- F capacitor?
A) 68 C
B) 90 C
C) 240 C
D) 180 C
E) 120 C
Q3) A combination of 2.0 in series with 4.0 is connected in parallel with 3.0 . What is the equivalent resistance?
Q4) Four 20. resistors are connected in parallel. What is the equivalent resistance?
Q5) List two conditions for producing an electric current in a circuit.
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Q1) An electron moving perpendicular to a magnetic field of 2.2 × 10<sup>-2</sup> T moves in a circle of certain radius. If the electron is moving with a speed of 1.5 × 10<sup>7</sup> m/s, what is the radius of the circle?
A) 1.5 × 10<sup>-3</sup> m
B) 2.2 × 10<sup>-4</sup> m
C) 2.2 × 10<sup>-3</sup>m
D) 3.9 × 10<sup>-4</sup> m
E) 3.9 × 10<sup>-3</sup> m
Q2) A rectangular loop of wire, with dimensions shown in Figure 22-8, carries a current of 2 A and is placed in a magnetic field of 0.8 T. The wire rotates in the magnetic field and at one point it is perpendicular to the magnetic field. What is the magnitude of the torque acting on the wire?
A) 0 Nm
B) 1 Nm
C) 2 Nm
D) 3 Nm
E) 4 Nm
Q3) Describe diamagnetism.
Q4) Describe ferromagnetism.
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Q1) Suppose that you wish to construct a simple AC generator with an output of 12. V maximum when rotated at 60. Hz. A magnetic field of 0.050 T is available. If the area of the rotating coil is 100. cm<sup>2</sup>, how many turns are needed?
Q2) A transformer with 120. turns in its secondary supplies 12. volts at 220. ma to a toy train. The primary is connected across a 120. V wall outlet.
(a) How many turns are in the primary?
(b) What is the primary current?
(c) What power is delivered by the wall outlet?
Q3) A coil of 40. turns and cross-sectional area 12. cm<sup>2</sup> is oriented perpendicular to a magnetic field, which varies from zero to 1.2 T in 0.02 s. What emf is induced in the coil?
Q4) There is an induced emf in a wire that is moving parallel to a magnetic field if the wire is moving in the opposite direction to that of the magnetic field.
A)True
B)False
Q5) State Lenz's Law.
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Q1) The total impedance of an RC circuit with a resistance of 200 is 1060 . If the frequency of the applied voltage is 20.0 Hz, what is the value of the capacitance in this circuit?
A) 6.64 F
B) 7.64 F
C) 8.64 F
D) 9.64 F
E) 200 F
Q2) A 200- resistor, a 25-mH inductor, and a capacitor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 240 , what is the value of the capacitor?
A) 5.5 F
B) 3.2 F
C) 4.2 F
D) 6.5 F
E) 7.5 F
Q3) In a series RLC circuit a capacitor will be dominant at lower frequencies.
A)True
B)False
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Q1) In Fizeau's experiment for measuring the speed of light, the wheel has 475 notches. What rotational speed is required for the return beam of light to pass through the next notch? The time between successive notches is 6.65 × 10<sup>-5</sup> s.
A) 20.4 rev/sec
B) 16.6 rev/sec
C) 31.7 rev/sec
D) 66.4 rev/sec
E) 90.9 rev/sec
Q2) Electromagnetic waves do not require a medium to be transmitted.
A)True
B)False
Q3) A radio station broadcasts at a frequency of 80 MHz. How far will this signal travel in 67 ms?
A) 60 × 10<sup>6</sup> m
B) 67 m
C) 40 × 10<sup>6</sup> m
D) 80 m
E) 20 × 10<sup>6</sup> m
Q4) A cordless phone operates at 900 MHz. What is the associated wavelength?
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Q1) A ray of light in air enters a glass surface at right angles to the surface. What is the angle of incidence?
A) 0°
B) 90°
C) 180°
D) 270°
E) 360°
Q2) A concave mirror is also known as a diverging mirror.
A)True
B)False
Q3) A 4.0-cm-tall object is placed 50.0 cm from a diverging lens of focal length 25.0 cm. What is the nature and location of the image?
A) A real image, 4.0 cm tall, 20 cm other side of the object
B) A virtual image, 4.0 cm tall, 20 cm other side of the object
C) A virtual image, 2.0 cm tall, 10 cm other side of the object
D) A virtual image, 1.3 cm tall, 16.7 cm same side as the object
E) A real image, 1.3 cm tall, 16.7 cm same side as the object
Q4) Magnification is positive for inverted images.
A)True
B)False

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Q1) Which one of the following is a characteristic of a compound microscope?
A) The objective is a diverging lens.
B) The eyepiece is a diverging lens.
C) The final image is real.
D) The image formed by the objective is virtual.
E) The image formed by the objective is real.
Q2) What is the power of the lens that has a focal length of 40 cm?
A) -2.5 diopters
B) -4.0 diopters
C) +4.0 diopters
D) +2.5 diopters
E) +2.7 diopters
Q3) The focal length of a lens is 5 m. What is the refractive power of this lens in diopters?
A) 0.1 diopters
B) 0.2 diopters
C) 0.3 diopters
D) 0.4 diopters
E) 0.5 diopters
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Q1) When a beam of light, which is traveling in glass, strikes an air boundary, there is
A) a 90° phase change in the reflected beam.
B) no phase change in the reflected beam.
C) a 180° phase change in the reflected beam.
D) a 60° phase change in the reflected beam.
E) a 45° phase change in the reflected beam.
Q2) A single-slit diffraction pattern is formed on a distant screen. Assuming the angles involved are small, by what factor will the width of the central bright spot on the screen change if the wavelength is doubled?
A) It will be cut to one-quarter its original size.
B) It will be cut in half.
C) It will double.
D) It will become four times as large.
E) It will become eight times as large.
Q3) In the two-slit experiment, for the condition of dark fringes, the value of m = +2 corresponds to a path difference of 3 /2.
A)True
B)False
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Questions
Q1) A spaceship approaches Earth with a speed 0.38c. A passenger in the spaceship measures his heartbeat as 72 beats per minute. How many beats per minute are observed in the telemetry radio signals received on Earth? Note that, in addition to time dilation, one must take into account that the signals of successive heartbeats have to travel shorter distances because the spaceship is moving closer (Doppler Effect).
A) 75
B) 107
C) 48
D) 100
E) 67
Q2) An object moves in a direction parallel to its length with a velocity that approaches the velocity of light. The length of this object, as measured by a stationary observer, A) approaches infinity. B) approaches zero. C) increases slightly.
D) decreases slightly.
E) does not change.
Q3) What is meant by proper length?
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Q1) Which one of the following is the correct expression for the Heisenberg uncertainty principle?
A) p<sub>y</sub> y h/2
B) p<sub>y</sub> y h/2
C) p<sub>y</sub>/ y h/2
D) y/ p<sub>y</sub> h/2
E) None of the other answers is correct.
Q2) X-rays with a wavelength of 0.00100 nm are scattered by free electrons at 130°. What is the kinetic energy of each recoil electron?
Q3) The wavelength of a light beam is doubled. Which one of the following is correct for the momentum of photons for that light beam?
A) It is halved.
B) It stays the same.
C) It is doubled.
D) It is reduced by one-fourth
E) It is quadrupled.
Q4) An electron is trapped in a box of width 0.10 nm. What is the wavelength of the photon emitted when an electron makes a transition from the n = 3 to the n = 1 state?
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Q1) A certain laser radiates with a wavelength of 2488 nm. What is the energy difference, in electron volts, between the two energy levels involved in producing this light?
A) 0.50 eV
B) 0.65 eV
C) 0.45 eV
D) 0.60 eV
E) 0.55 eV
Q2) Ernest Rutherford tested Thomson's model by directing a beam of beta particles, at a thin gold foil.
A)True
B)False
Q3) What type of spectrum is produced when a high energy electron beam is incident on a metal target producing X-rays?
A) line spectrum
B) emission spectrum
C) absorption spectrum
D) continuous spectrum
E) line spectrum superimposed on a continuous spectrum
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Q1) Francium-223 decays to radium-223 by emitting what kind of nuclear radiation?
A) Alpha
B) Beta minus C) Beta plus D) Gamma
E) X-rays.
Q2) Elementary particles that experience the weak nuclear force but not the strong force are called A) leptons.
B) hadrons. C) mesons. D) bosons.
E) baryons.
Q3) If a nuclide has a decay constant of 0.765 × 10<sup>-</sup><sup>6</sup> s<sup>-1</sup> and contains 3.0 × 10<sup>17</sup> nuclei
(a) what is the half life?
(b) what is its initial activity?
(c) what is the activity after 12. days?
Q4) What is the approximate nuclear radius of an isotope of sodium with 11 protons and 12 neutrons?
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