Question 1

The speed of light is equal to

Accepted Answer

A) 5.28 × 107 miles per hour. 
B) one meter per nanosecond. 
C) one light-year per year. 
D) none of the above. 
A) 5.28 × 107 miles per hour. 
B) one meter per nanosecond. 
C) one light-year per year. 
D) none of the above.

Question 2

An astronaut at rest has a heart rate of 68 beats/min.What will her heart rate be as measured by an Earth observer when the astronaut's spaceship goes by the Earth at a speed of 0.76c?

Accepted Answer

A) 105 beats/min 
B) 52 beats/min 
C) 33 beats/min 
D) 139 beats/min 
E) ​44 beats/min 
A) 105 beats/min 
B) 52 beats/min 
C) 33 beats/min 
D) 139 beats/min 
E) ​44 beats/min

Question 3

An astronaut is traveling at a high rate of speed from the Earth to a distant star system.Observers here on Earth note the relativistic effect that the astronaut's clocks run slow.What relativistic effect,if any,does the astronaut observe?

Accepted Answer

A) Her pulse rate slows. 
B) The distance from the Earth to the star system has decreased. 
C) Her clocks run faster. 
D) There is no relativistic effect to be observed by the astronaut since she is the one doing the moving. 
A) Her pulse rate slows. 
B) The distance from the Earth to the star system has decreased. 
C) Her clocks run faster. 
D) There is no relativistic effect to be observed by the astronaut since she is the one doing the moving.

Question 4

According to the special theory of relativity,which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?

Accepted Answer

A) interval increases 
B) interval decreases 
C) interval remains constant 
D) interval vanishes to zero when velocity equals half speed of light 
A) interval increases 
B) interval decreases 
C) interval remains constant 
D) interval vanishes to zero when velocity equals half speed of light

Question 5

How fast would a rocket have to move past a ground observer if the latter were to observe a 9.4% length shrinkage in the rocket length? (c = 3.00 × 108 m/s)

Accepted Answer

A) 2.98 × 108 m/s 
B) 2.72 × 108 m/s 
C) 1.27 × 108 m/s 
D) 0.420 × 108 m/s 
E) ​0.920 × 108 m/s 
A) 2.98 × 108 m/s 
B) 2.72 × 108 m/s 
C) 1.27 × 108 m/s 
D) 0.420 × 108 m/s 
E) ​0.920 × 108 m/s

Question 6

A space probe has a 24.7-m length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.860c?

Accepted Answer

A) 25.2 m 
B) 6.43 m 
C) 9.19 m 
D) 12.6 m 
A) 25.2 m 
B) 6.43 m 
C) 9.19 m 
D) 12.6 m

Question 7

What is the total energy of a proton moving at a speed of 2.4 × 108 m/s? (proton mass is 1.67 × 10−27 kg and c = 3.00 × 108 m/s)

Accepted Answer

A) 1.91E-10 J 
B) 1.77E-10 J 
C) 2.51E-10 J 
D) 2.44E-10 J 
E) ​9.02E-11 J 
A) 1.91E-10 J 
B) 1.77E-10 J 
C) 2.51E-10 J 
D) 2.44E-10 J 
E) ​9.02E-11 J

Question 8

As measured from the Earth,a spacecraft is moving at speed 0.80c toward another spacecraft moving at speed 0.60c in the same direction,i.e. ,the first spacecraft is catching up with the second spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

Accepted Answer

A) 0.38c 
B) -0.20c 
C) -0.38c 
D) not given 
A) 0.38c 
B) -0.20c 
C) -0.38c 
D) not given

Question 9

According to a postulate of Einstein,which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?

Accepted Answer

A) Laws are same only in inertial frames with zero velocity. 
B) Laws are same only in inertial frames moving at low velocities. 
C) Laws are same only in inertial frames moving at near speed of light. 
D) Laws are same in all inertial frames. 
A) Laws are same only in inertial frames with zero velocity. 
B) Laws are same only in inertial frames moving at low velocities. 
C) Laws are same only in inertial frames moving at near speed of light. 
D) Laws are same in all inertial frames.

Question 10

If astronauts could travel at v = 0.95c,we on Earth would say it takes (4.2/0.95)= 4.4 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

Accepted Answer

A) 1.4 years 
B) 14.1 years 
C) 4.0 years 
D) 1.3 years 
E) ​0.4 years 
A) 1.4 years 
B) 14.1 years 
C) 4.0 years 
D) 1.3 years 
E) ​0.4 years

Question 11

An electron of mass 9.11 × 10−31 kg moves with a speed of 0.660c.What is its kinetic energy? (c = 3.00 × 108 m/s)

Accepted Answer

A) 2.71E-14 J 
B) 1.09E-13 J 
C) 8.20E-14 J 
D) 1.79E-14 J 
E) ​2.04E-14 J 
A) 2.71E-14 J 
B) 1.09E-13 J 
C) 8.20E-14 J 
D) 1.79E-14 J 
E) ​2.04E-14 J

Question 12

If a proton with mass 1.67 × 10−27 kg moves in an accelerator such that its total energy is three times its rest energy,what is its speed? (c = 3.00 × 108 m/s)

Accepted Answer

A) 2.83 × 108 m/s 
B) 2.45 × 108 m/s 
C) 2.00 × 108 m/s 
D) 1.00 × 108 m/s 
E) ​1.54 × 108 m/s 
A) 2.83 × 108 m/s 
B) 2.45 × 108 m/s 
C) 2.00 × 108 m/s 
D) 1.00 × 108 m/s 
E) ​1.54 × 108 m/s

Question 13

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be five times its rest energy? (me = 9.11 × 10-31 kg,c = 3.00 × 108 m/s,and qe = 1.6 × 10−19 C)

Accepted Answer

A) 1.6E-19 V 
B) 2.6E+6 V 
C) 2.0E+6 V 
D) 210 V 
E) ​6.8E-3 V 
A) 1.6E-19 V 
B) 2.6E+6 V 
C) 2.0E+6 V 
D) 210 V 
E) ​6.8E-3 V

Question 14

When a one-megaton nuclear bomb is exploded,approximately 4.0 × 1015 J of energy is released.How much mass would this represent in a mass-to-energy conversion? (c = 3.00 × 108 m/s)

Accepted Answer

A) 1.333 × 106 kg 
B) 0.044 kg 
C) 0.444 kg 
D) 3.600 kg 
E) ​4.0 × 103 kg 
A) 1.333 × 106 kg 
B) 0.044 kg 
C) 0.444 kg 
D) 3.600 kg 
E) ​4.0 × 103 kg

Question 15

According to the special theory of relativity,which of the following happens to the length of an object,measured in the dimension parallel to the motion of its inertial frame of reference,as the velocity of this frame increases with respect to a stationary observer?

Accepted Answer

A) length increases 
B) length decreases 
C) length remains constant 
D) length vanishes to zero when velocity equals half speed of light 
A) length increases 
B) length decreases 
C) length remains constant 
D) length vanishes to zero when velocity equals half speed of light

Question 16

That the speed of light in a vacuum has the same value for all inertial frames is

Accepted Answer

A) inconsistent with the results of the Michelson-Morley experiment. 
B) consistent with the results of the Michelson-Morley experiment. 
C) not related to the results of the Michelson-Morley experiment. 
D) not true. 
A) inconsistent with the results of the Michelson-Morley experiment. 
B) consistent with the results of the Michelson-Morley experiment. 
C) not related to the results of the Michelson-Morley experiment. 
D) not true.

Question 17

If the total energy of an electron in an accelerator is three times its rest energy,what is its speed? (c = 3.00 × 108 m/s)

Accepted Answer

A) 2.00 × 108 m/s 
B) 1.30 × 108 m/s 
C) 1.41 × 108 m/s 
D) 2.98 × 108 m/s 
E) ​2.83 × 108 m/s 
A) 2.00 × 108 m/s 
B) 1.30 × 108 m/s 
C) 1.41 × 108 m/s 
D) 2.98 × 108 m/s 
E) ​2.83 × 108 m/s

Question 18

As measured from the Earth,a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction.What would be the speed of the probe as measured from the Earth?

Accepted Answer

A) 0.70c 
B) 0.81c 
C) c 
D) 0.95c 
A) 0.70c 
B) 0.81c 
C) c 
D) 0.95c

Question 19

What is the speed of a particle having a kinetic energy equal to its rest energy?

Accepted Answer

A) The mass of the particle must be given since the answer can only be given in terms of the mass. 
B)    
C)    
D)    
A) The mass of the particle must be given since the answer can only be given in terms of the mass. 
B)    
C)    
D)

Question 20

A rocket ship is 87.0 m in length when measured before leaving the launching pad.What would its velocity be if a ground observer measured its length as 62.0 m while it is in flight? (c = 3.00 × 108 m/s)

Accepted Answer

A) 1.61 × 108 m/s 
B) 2.14 × 108 m/s 
C) 1.48 × 108 m/s 
D) 2.10 × 108 m/s 
E) ​1.91 × 108 m/s 
A) 1.61 × 108 m/s 
B) 2.14 × 108 m/s 
C) 1.48 × 108 m/s 
D) 2.10 × 108 m/s 
E) ​1.91 × 108 m/s

Exam 26: Relativity

The speed of light is equal to

An astronaut at rest has a heart rate of 68 beats/min.What will her heart rate be as measured by an Earth observer when the astronaut's spaceship goes by the Earth at a speed of 0.76c?

An astronaut is traveling at a high rate of speed from the Earth to a distant star system.Observers here on Earth note the relativistic effect that the astronaut's clocks run slow.What relativistic effect,if any,does the astronaut observe?

According to the special theory of relativity,which of the following happens to the size of the time interval between two events occurring in an inertial frame of reference as the frame's velocity with respect to the observer increases?

How fast would a rocket have to move past a ground observer if the latter were to observe a 9.4% length shrinkage in the rocket length? (c = 3.00 × 108 m/s)

A space probe has a 24.7-m length when measured at rest.What length does an observer at rest measure when the probe is going by at a speed of 0.860c?

What is the total energy of a proton moving at a speed of 2.4 × 108 m/s? (proton mass is 1.67 × 10−27 kg and c = 3.00 × 108 m/s)

As measured from the Earth,a spacecraft is moving at speed 0.80c toward another spacecraft moving at speed 0.60c in the same direction,i.e. ,the first spacecraft is catching up with the second spacecraft.What is the speed of the first spacecraft as viewed from the second spacecraft?

According to a postulate of Einstein,which of the following describes the nature of the laws of physics as one observes processes taking place in various inertial frames of reference?

If astronauts could travel at v = 0.95c,we on Earth would say it takes (4.2/0.95)= 4.4 years to reach Alpha Centauri,4.2 lightyears away.The astronauts disagree.How much time passes on the astronaut's clocks?

An electron of mass 9.11 × 10−31 kg moves with a speed of 0.660c.What is its kinetic energy? (c = 3.00 × 108 m/s)

If a proton with mass 1.67 × 10−27 kg moves in an accelerator such that its total energy is three times its rest energy,what is its speed? (c = 3.00 × 108 m/s)

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be five times its rest energy? (me = 9.11 × 10-31 kg,c = 3.00 × 108 m/s,and qe = 1.6 × 10−19 C)

When a one-megaton nuclear bomb is exploded,approximately 4.0 × 1015 J of energy is released.How much mass would this represent in a mass-to-energy conversion? (c = 3.00 × 108 m/s)

According to the special theory of relativity,which of the following happens to the length of an object,measured in the dimension parallel to the motion of its inertial frame of reference,as the velocity of this frame increases with respect to a stationary observer?

That the speed of light in a vacuum has the same value for all inertial frames is

If the total energy of an electron in an accelerator is three times its rest energy,what is its speed? (c = 3.00 × 108 m/s)

As measured from the Earth,a spacecraft is moving at speed 0.80c when it releases a probe at speed 0.60c relative to the spacecraft in a forward direction.What would be the speed of the probe as measured from the Earth?

What is the speed of a particle having a kinetic energy equal to its rest energy?

A rocket ship is 87.0 m in length when measured before leaving the launching pad.What would its velocity be if a ground observer measured its length as 62.0 m while it is in flight? (c = 3.00 × 108 m/s)

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How fast would a rocket have to move past a ground observer if the latter were to observe a 9.4% length shrinkage in the rocket length? (c = 3.00 × 10⁸ m/s)

What is the total energy of a proton moving at a speed of 2.4 × 10⁸ m/s? (proton mass is 1.67 × 10−²⁷ kg and c = 3.00 × 10⁸ m/s)

An electron of mass 9.11 × 10−³¹ kg moves with a speed of 0.660c.What is its kinetic energy? (c = 3.00 × 10⁸ m/s)

If a proton with mass 1.67 × 10−²⁷ kg moves in an accelerator such that its total energy is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

Through what potential difference would an electron initially at rest need to be accelerated to have its total energy be five times its rest energy? (m_e = 9.11 × 10^-31 kg,c = 3.00 × 10⁸ m/s,and q_e = 1.6 × 10−¹⁹ C)

When a one-megaton nuclear bomb is exploded,approximately 4.0 × 10¹⁵ J of energy is released.How much mass would this represent in a mass-to-energy conversion? (c = 3.00 × 10⁸ m/s)

If the total energy of an electron in an accelerator is three times its rest energy,what is its speed? (c = 3.00 × 10⁸ m/s)

A rocket ship is 87.0 m in length when measured before leaving the launching pad.What would its velocity be if a ground observer measured its length as 62.0 m while it is in flight? (c = 3.00 × 10⁸ m/s)