Physics Unit26: Special Theory of Relativity - 题库网 (tiku.one)

?作业考试练习?通用国际物理?Physics Unit26: Special Theory of Relativity

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习题练习：Physics Unit26: Special Theory of Relativity

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1#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

You are riding in a spaceship that has no windows, radios, or other means fotn vnw eu-y5 a.r:s8an qxz(8/r you to observz8 rewa a. vn8syxu/5-(qt:nne or measure what is outside. You wish to determine if the ship is stopped or moving at constant velocity. What should you do?

A. You can determine if the ship is moving by determining the apparent velocity of light.

B. You can determine if the ship is moving by checking your precision time piece. If it's running slow, the ship is moving.

C. You can determine if the ship is moving either by determining the apparent velocity of light or by checking your precision time piece. If it's running slow, the ship is moving.

D. You should give up because you have taken on an impossible task.

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2#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The Michelson-Morley experiment was designed to measur.o.d sv4nt5u4nhle ,i e

A. the relativistic mass of the electron.

B. the relativistic energy of the electron.

C. the velocity of the Earth relative to the ether.

D. the acceleration of gravity on the Earth's surface.

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3#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Michelson and Morley concluded from/,f xtk,fl *tf the results of their experiment that

A. the experiment was a failure since there was no detectable shift in the interference pattern.

B. the experiment was successful in not detecting a shift in the interference pattern.

C. the experiment was a failure since they detected a shift in the interference pattern.

D. the experiment was successful in detecting a shift in the interference pattern.

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4#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

You can build an intercph)(l5rm5a zn pba;9n /ttq8ferometer yourself if you use the following components:

A. a light source, a detector screen, a partially silvered mirror, a flat mirror, and a glass plate.

B. a light source, a detector screen, two partially silvered mirrors, and a glass plate.

C. a light source, a detector screen, two partially silvered mirrors, a flat mirror, and a glass plate.

D. a light source, a detector screen, a partially silvered mirror, two flat mirrors, and a glass plate.

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5#

问答题 ( 1.0 分) 切至整卷模式搜藏此题

State the relativity princkb1/5p qfa0 lykt(sl5iple.

该题自我估分: (必填) (满分:1.0分)

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6#

问答题 ( 1.0 分) 切至整卷模式搜藏此题

State the three unprovable assumptions lg6 0a6a2v/cr o 7 lqnyx4w0qyof Galilean-Newtonian relativity.

该题自我估分: (必填) (满分:1.0分)

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7#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The theory of special relcw*.vdqb24,n8b0dnr eqfk3 w- w7d blativity

A. is based on a complex mathematical analysis.

B. has not been verified by experiment.

C. does not agree with Newtonian mechanics.

D. does not agree with electromagnetic theory.

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8#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

One of Einstein's postulates in formulating the special theoryv +1a(u x1sigr of relativity was that the laws of physics are the sam11s(uxga ri+ ve in reference frames that

A. accelerate.

B. move at constant velocity with respect to an inertial frame.

C. oscillate.

D. are stationary, but not in moving frames.

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9#

问答题 ( 1.0 分) 切至整卷模式搜藏此题

State the first postulate of special relativ-q*gpq. lc58e/ kt8 hec.h viaity.

该题自我估分: (必填) (满分:1.0分)

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10#

问答题 ( 1.0 分) 切至整卷模式搜藏此题

State the second postulate of spejgcdjx1hu/+d+)v- l0yqe. m5jt nf )dcial relativity.

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11#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

If you were to measure your pulse rate while in a spaceship moving away from ay.nzm7x/ uu ;the Sunamz./u yun; 7x at a speed close to the speed of light, you would find that it was

A. much faster than normal.

B. much slower than normal.

C. the same as it was here on Earth.

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12#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Relative to a stationary obserc+a egb r pwt,;0qn2l1ver, a moving clock

A. always runs slower than normal.

B. always runs faster than normal.

C. keeps its normal time.

D. can do any of the above. It depends on the relative velocity between the observer and the clock.

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13#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The gamma factor is defi-pj6uqeamv( oulss7 2:; kqc,ned as $\gamma = 1 / \sqrt{1- (v/c)^2}$, therefore gamma ($\gamma$)

A. can be zero.

B. can be any number less than or equal to one.

C. can be any number greater than or equal to one.

D. cannot equal one.

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14#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Suppose one twin takes a ridcrjo+ -, -+myr f*w9hu iwcn.me in a space ship traveling at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Earth pred9ci jw-.+rf* mn,oruc +mh-wyicts that the astronaut twin is

A. younger.

B. the same age.

C. older.

D. cannot be determined from the given information

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15#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Relative to a stationary observer, a movinflgne: m cf801oka eifq5d040g object

A. appears shorter than normal.

B. appears longer than normal.

C. keeps its same length time.

D. can do any of the above. It depends on the relative velocity between the observer and the object.

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16#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

An object moves in a direction parallel to its length with a velocity tha,e:l rvptp v1+3bras) t approaches the velocity of light. The width of this object, as measure)+r s:,lr3 e1 ppvvbatd by a stationary observer,

A. approaches infinity.

B. approaches zero.

C. increases slightly.

D. does not change.

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17#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

An object moves in a direction parallel to its length with a velocity that appx*iy-q3k ;a n1p1jultroaches the velocity of light. The length of this object, as measured by p*t3q1 nlyua1 kxj;i-a stationary observer,

A. approaches infinity.

B. approaches zero.

C. increases slightly.

D. does not change.

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18#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

As the speed of a particle approko1xzvp0;z tg k,wnr2 j t6a76aches the speed of light, the mass of the particle 7k;vro0ng2zzaj1t6twk,xp6

A. increases.

B. decreases.

C. remains the same.

D. approaches zero.

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19#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

As the speed of a particle approaches the speed of light,edtp+0ojd)m, the momentum of the particled,tej0 od)mp+

A. increases.

B. decreases.

C. remains the same.

D. approaches zero.

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20#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A spear is thrown by you at a very high speed. zi07hv u x,m799vda2 x1lxrem As it passes, you measure its length at one-half ith9xzlv2d0e 1, m9ui 7xvmrxa7 s normal length. From this measurement, you conclude that the moving spear's mass must be

A. one-half its rest mass.

B. twice its rest mass.

C. four times its rest mass.

D. none of the given answers

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21#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What happens to the kinetic energy of a spe7u tpp r0w,qw+edy proton when its relativistic mass doubl 7 rqu,ptp0ww+es?

A. It doubles.

B. It more than doubles.

C. It less than doubles.

D. It must increase, but it is impossible to say by how much.

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22#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What happens to the total relativistic energy of a s. f)+peoxq5 abpeedy proton when its relativistic mass doubpqb+.xf a )eo5les?

A. It doubles.

B. It more than doubles.

C. It less than doubles.

D. It must increase, but it is impossible to say by how much.

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23#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Consider a particle of ma z xtu8ct,lr 02xbbrb y-7(c7tss $m$ and rest mass $m_0$. Which of the following is the correct expression for the kinetic energy of such a particle?

A. $\frac{1}{2} m_0 v^2$

B. $\frac{1}{2} m v^2$

C. $m c^2 - m_0 c^2$

D. $\frac{1}{2}(mc^2 - m_0 c^2)$

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24#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Consider two spaceships, each traveling at 0.50c in a strnc eb 3,h udxq7g2/z+gaight line. Ship A is moving directly away 7uqnx+,bcz /d 3 gh2gefrom the Sun and ship B is approaching the Sun. The science officers on each ship measure the velocity of light coming from the Sun. What do they measure for this velocity?

A. Ship A measures it as less than c, and ship B measures it as greater than c.

B. Ship B measures it as less than c, and ship A measures it as greater than c.

C. On both ships it is measured to be less than c.

D. On both ships it is measured to be exactly c.

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25#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Which of the following depends on the observer's f8urukkjew8)q 5q.zk 7e) .,vd o*t xqrrame of reference?

A. the mass of the proton

B. the length of a meter stick

C. the half-life of a muon

D. all of the given answers

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26#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

As the velocity of your spaceship increasesrn3qoww ,sum9yakkx;u0w;,, , you would observe

A. that your precision clock runs slower than normal.

B. that the length of your spaceship has decreased.

C. that your mass has increased.

D. all of the given answers

E. none of the given answers

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27#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A boat can travel 4.0 m/s in still water. With what speed, relativecu; 20 1jqf+iuc u+qkr to the shore, doeir cq0;j2uf ++u1uqcks it move in a river that is flowing at 1.0 m/s if the boat is heading upstream?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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28#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A boat can travel 4.0 m/s in still water. With wd; gs/a1 + ya/rfckot0ope 3 )gox3tf+hat speed, relative to the shore, does g /o0ok /a)+ftfy13rg3;ed+cpxt s ao it move in a river that is flowing at 1.0 m/s if the boat is heading downstream?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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29#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A boat can travel 4.0 :hks w:- 3bccyt(a9 .8sjydvpm/s in still water. With what speed, relative to the shore, does it move in a river that 9pcc ybs-83(ks .ajvdt:wyh:is flowing at 1.0 m/s if the boat is heading straight across the river?

A. 3.0 m/s

B. 4.1 m/s

C. 4.8 m/s

D. 5.0 m/s

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30#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

How fast should a moving clock 1tx2pbwr,u c229vbwo travel if it is to be observed by a stationary observer au 2wotv2wbr, 2b9 pc1xs running at one-half its normal rate?

A. $0.50 \; c$

B. $0.65 \; c$

C. $0.78 \; c$

D. $0.87 \; c$

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31#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A spaceship takes a y 5oug7,2sq1ysc tahu4 + xoi/nonstop journey to a planet and returns in 10 hours accordingoh,17c+ 4itxyasgq/ y5uo s2u to a clock on the spaceship. If the speed of the spaceship is 0.80c, how much time has elapsed on the Earth?

A. $3.2 \; h$

B. $7.0 \; h$

C. $15 \; h$

D. $17 \; h$

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32#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A set of twins, Andrea and Courtney, are initiall/. 0xv ay7c gdx14xnmhy 10 years old. While Courtney remains on Earth, Andrea rides on a space ship which travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and congm0h/74d xcxy 1.axv mes back at 0.6c. When Andrea returns, Courtney is 20 years old. How old is Andrea upon her return?

A. $10 \; years$

B. $12 \; years$

C. $18 \; years$

D. $20 \; years$

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33#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

One 20-year-old twin brother takesbq8h)rkdv m23 mk0yy / a space trip with a speed of 0.80c for 30 years according to a clock on ther82bd )/k m kq0m3yyhv spaceship. Upon returning to the Earth, what is his own age and the age of the Earth-based twin brother?

A. 20; 30

B. 30; 50

C. 50; 70

D. 70; 90

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34#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A meter stick is moving toward you w18 jco xo01tqc;y -sgqith a speed of 0.80c. What is its length?

A. zero

B. $0.40 \; m$

C. $0.60 \; m$

D. $1.0 \; m$

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35#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

How fast would a rocket ship have to mov1tlx1s2 p-(,nt a kc8f4js,mquk xy q1e to contract to half of its proper lengths ut-knqsfc 11 a4yxmt 2q,(kp,j 1xl8 (as observed by a stationary object)?

A. $0.50 \; c$

B. $0.65 \; c$

C. $0.78 \; c$

D. $0.87 \; c$

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36#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The length of a spaceship is 10 m when itj;t-6fl sz )f)dkik1c vsr:7g is at rest. If the spaceship travels by you wkc7k 1sff 6sl)gt- ;r:ij)dzv ith a speed of 0.70c, what length does it appear to you?

A. $5.5 \; m$

B. $7.1 \; m$

C. $12 \; m$

D. $18 \; m$

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37#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The closest star to our solar syst mql(2e4 99fn+ 4,m; yqfav c*whj07yria tjopem is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. What distance does fp lmvrjqw0n (2mat7yih*4e9y+ j;fqc ao49,the space ship travel according to a passenger on the ship?

A. $2.58 \; ly$

B. $3.52 \; ly$

C. $4.12 \; ly$

D. $4.30 \; ly$

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38#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The closest star to our solar system is Alpha Centauri, which is 4.3fx 7+t3jq8nl6/uwg l ai +za,o0 light years away. A spaceship with a constant speed of 0.800c relwa8i/u l7+ +tngl jxz ,of36qaative to the Earth travels toward the star. How much time would elapse on a clock on board the spaceship?

A. $3.23 \; y$

B. $4.40 \; y$

C. $5.15 \; y$

D. $5.38 \; y$

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39#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The closest star to our solar system is Alpha Ce5 o+d2df ye5nt kyex( 0smg(:pntauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much y: d0(25(t+ekogd sypf 5n xemtime would elapse on a clock on the Earth?

A. $3.23 \; y$

B. $4.40 \; y$

C. $5.15 \; y$

D. $5.38 \; y$

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40#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

An electron is traveling at 0.xvw8 0m;o5d j2ffter085c. What is its mass? (The rest mass is $9.11 \times 10^{-31} \; kg$.)

A. $1.4 \times 10^{-29} \; kg$

B. $7.2 \times 10^{-30} \; kg$

C. $1.7 \times 10^{-30} \; kg$

D. $2.4 \times 10^{-30} \; kg$

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41#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What is the speed of a proton if its mass is twice its r)(f8 /n1sdw ofb2x 6vtg) pxaaest mass?

A. $0.50 \; c$

B. $0.68 \; c$

C. $0.73 \; c$

D. $0.87 \; c$

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42#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

If the velocity of yovddrj,np7 h y h/5joyb ,o5),eur spaceship goes from 0.3 c to 0.6 c, then your mass will increanv j dpo 5 7,,j5e)h/yh,oybdrse by

A. 19%.

B. 38%.

C. 100%.

D. 200%.

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43#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What is the momentum b,,:rm/cnjxgtt xv43 in $kg \cdot m/s$ of a proton when it is moving with a speed of 0.60c?

A. $1.2 \times 10^{-19} \; kg \cdot m/s$

B. $1.5 \times 10^{-19} \; kg \cdot m/s$

C. $3.0 \times 10^{-19} \; kg \cdot m/s$

D. $3.8 \times 10^{-19} \; kg \cdot m/s$

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44#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

During a reaction, an elemen-7o lnjmew8y 3t loses $4.8 \times 10^{-28} \; kg$ of mass. How much energy (in Joules) is released?

A. $4.3 \times 10^{-11} \; J$

B. $1.4 \times 10^{-19} \; J$

C. $1.6 \times 10^{-36} \; J$

D. $5.3 \times 10^{-45} \; J$

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45#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

During a reaction, $1.7 \times 10^{-4} \; J$ of energy is released. What change of mass would cause this?

A. $5.1 \times 10^{-4} \; kg$

B. $1.5 \times 10^{-13} \; kg$

C. $4.8 \times 10^{-18} \; kg$

D. $1.9 \times 10^{-21} \; kg$

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46#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

How much energy would be released if 2.0 kg of material was lost during a reactlh0mih1 a;w7 si him a;l701swhon?

A. $1.8 \times 10^{17} \; J$

B. $1.5 \times 10^{16} \; J$

C. $6.0 \times 10^{8} \; J$

D. $4.7 \times 10^{-8} \; J$

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47#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The amount of energy equivalent to two kilogram of mass at rest i-d*mjubm.(rn9wz 2sny:- a db s

A. $18 \times 10^{16} \; J$.

B. $3.0 \times 10^{8} \; J$.

C. $9.0 \times 10^{16} \; J$.

D. none of the given answers

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48#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The atomic bomb that was dropped on Na( m4 0fl)h,ry4rcgf-o9n bidj gasaki in 1945 killed 140,000 people, helping to end World War II on the next day. It released energy equivalent to that of 20,000 tons of TNT explosive. Howm i 49b4gfrcf(ljy) -,ro0hdn much mass was converted to energy when this took place? (1000 tons of TNT = $4.3 \times 10^{12} \; J$) Incidentally, modern H-bombs have energy yields 1000 times as much!

A. $1 \; g$

B. $10 \; g$

C. $100 \; g$

D. $1 \; kg$

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49#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The kinetic energy of a proton is 80% of its total energy. c.1rmhl*1e ce:xk(q p What is the speed of th.lxcc h 1prk(e :mq*1ee proton?

A. $0.02 \; c$

B. $0.87 \; c$

C. $0.98 \; c$

D. $1.0 \; c$

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50#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

The kinetic energy of a proton is 80% of its total enerxg) uzsctv5h,z l.(j8gy. What is the momentum hsz)j,.(zc5t8gu lxvin $kg \cdot m/s$ of the proton?

A. $5.0 \times 10^{-19} \; kg \cdot m/s$

B. $2.5 \times 10^{-19} \; kg \cdot m/s$

C. $5.0 \times 10^{-18} \; kg \cdot m/s$

D. $2.5 \times 10^{-18} \; kg \cdot m/s$

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51#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What energy is released (in MeV) during a reac5k/+ a3vt8ctopg xc o5tion in which $1.67 \times 10^{-25} \; kg$ of material is converted to energy?

A. $5.0 \times 10^{-14} \; MeV$

B. $4.1 \times 10^{-7} \; MeV$

C. $3.1 \times 10^{-4} \; MeV$

D. $9.4 \times 10^{4} \; MeV$

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52#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

How much mass is lost duru5v+j 8izsgvbdth7 04h-f8rc95ws q ping a reaction in which $1.7 \times 10^{8} \; MeV$ of energy is released?

A. $1.8 \times 10^{-8} \; kg$

B. $5.7 \times 10^{-9} \; kg$

C. $1.9 \times 10^{-17} \; kg$

D. $3.0 \times 10^{-22} \; kg$

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53#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

What is the total energy of an electrvjaf 3q5l mw1akans;tm h,40pf17go +on moving with a speed of 0.95c?

A. $2.6 \times 10^{-13} \; J$

B. $8.2 \times 10^{-14} \; J$

C. $1.1 \times 10^{-13} \; J$

D. $1.2 \times 10^{-14} \; J$

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54#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

How many joules of energy are required to accelerate one kilogram of mass f7woc 5jzy,qcp o1t (,qrom rest to a vel,w(cozotq ,7 c1jq5ypocity of 0.866 c?

A. $1.8 \times 10^{17} \; J$

B. $9.0 \times 10^{16} \; J$

C. $3.0 \times 10^{3} \; J$

D. none of the given answers

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55#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

In a nuclear plant, s9gea3qccrr6 22k93s q kt7n y$1017 J$ of energy is available from mass conversion. How much mass was lost?

A. $0.1 \; kg$

B. $1 \; kg$

C. $10 \; kg$

D. $100 \; kg$

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56#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

An electron is accelerated thz*j/b kv;nka(rough 100 kV. By what factor has its mass increased with respect to its rest mank va*zbk/ (;jss?

A. 1.20

B. 1.55

C. 4.25

D. 8.00

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57#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

You are in a rocket traveling away from the Sun at 0.95c. You )b6yz;lh *xbj n p,*esh*iwy0 measure the speed of light from the Sube zyh p;by0,*xh* jn )iw*l6sn to be

A. 0.05c.

B. 0.95c.

C. 1.0c.

D. cannot be determined without knowing the frequency of the light

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58#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

Two spaceships are trave ,j/ j/2sq jaoro4:wlbling through space at 0.60 c relative to the Earth. If the ships are headed directly toward each other, what is their approach velocity, as measured by a person onq joa/r,jos /j:bwl4 2 either craft?

A. $1.2 \; c$

B. $c$

C. $0.60 \; c$

D. none of the given answers

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59#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A fast spaceship is traveling with a speed of 0.80c. en qivlj:7l95How fast would light travel from the headlights of the ship relative to a stationary observei lq7vj95lne: r?

A. $0.20 \; c$

B. $0.80 \; c$

C. $1.0 \; c$

D. $1.8 \; c$

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60#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A spaceship moves away from the Earth with a speed of 0.80c. The spco n94s vf9k8spq0qfjjc27w+kd lys; ; m/s2 zaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the missile is fired away from the Earth?z9dwc4ns jqv;s+9qo7y2 2 0ls k; fc8jpm/ksf

A. $0.30 \; c$

B. $0.50 \; c$

C. $0.93 \; c$

D. $1.3 \; c$

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61#

单选题 ( 1.0 分) 切至整卷模式搜藏此题

A spaceship moves away from the Earth with a speed of 0hb;5u1x )xjn voy9lnr:9 a9gn.80c. The spaceship then fires a missile with a speed of 0.50c relative to the spaceship. What is the velocity of the missile measured by observers on the Earth if the mi)9n91nu 9hobnvg5 ;xla:y jxr ssile is fired toward the Earth?

A. $0.30 \; c$

B. $0.50 \; c$

C. $0.93 \; c$

D. $1.3 \; c$

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