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?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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答题人: 匿名未登录开始时间: 23年05月01日 10:24 切换到: 整卷模式

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 *t ntk8arc ao:, ;pb1qmeans for you to observe or measure what is outside. You wish to determine if the ship is stopped or moving at constant velocity. What shoqk*a;: rbt p81ctn,aould 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 wasc48pla gcuzy5 -m/ j+h designed to measure

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 the results of th4pf e ilbx,n(6eir 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 interferometer your6kt5c- g/lc ziw3 w7jaself 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 pri/tx(u s7l;xzd6v2gpmv )j8s enciple.

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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 of Galilean-Newtonian v2q-ziw8 c:w4tpi.c b h(ykl7relativity.

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 relativpt q6vr0xq;b4 ity

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 formulati qyhiyjwj,9.k6j/zay eo 393lng the special theory of relativity was that the laws of physics are the sa.qzj j9y ja9ohl3ey/6wy3k, ime 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 postulat 0adiv9tas1d;bm g4w 1e of special relativity.

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 special relat9+kgv.e vu *0 unrc1o oaw5s;livity.

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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*yqm kw u43/km a spaceship moving away from the Sun at a speed close to the speed 4myk* k 3wqmu/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 observer, axqjh)3l89*5 v gatw4gce.dan 9x(ept9 o7hgo 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 defined a: 1mcz vx();isa0hf gws $\gamma = 1 / \sqrt{1- (v/c)^2}$, 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 ride in a space ship travelinwuum 8j l91y n33q q.r:opppt5g at a very high speed to a distant star and back again, while the other twin remains on Earth. The twin that remained on Ealpu3.5tjpoq 9run3mp:w q8y1rth predicts 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 stationa . ul38jhp9us kw-rkqbc0( um;ry observer, a moving 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 th8cv +odtpv (ogtd 1*0yat approaches the velocity of light. The 1vcoty ogvpt 0+*(dd8 width of this object, as measured 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 wit yvs851-dvgjor 3ela/h a velocity that approaches the v-vgj3y8v e o 1la/d5rselocity of light. The length of this object, as measured by 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 approaches the speed of light, the mass of pzib 7 pa:*): ak-lqmdthe particleia-pbqa *):mk 7pz d:l

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 partjg 4yqh(ok/kq7yrs 0 /1zb-qaicle approaches the speed of light, the momentum of the paj/r 0q/hgo(ayq 4k1q z-ky 7bsrticle

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. As it passes, you measure its lec3ywfxuwqf)4 * h )a+gngth at one-half its normal length. From this mg+ hwcaw f*y )ufqx3)4easurement, 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 speedy proton when its relativ :ci q;t(p1grdistic mass doublesq 1p:(cdri;gt?

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 speedy protonqdb0 fb+u)2i bz vrr)h p065cj when its relativisdbhz +jcr pu0)f)rb q5v206bi tic mass doubles?

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 oy71hnsp. 6myqf mass $m$ 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, et(.i98y p cyqsach traveling at 0.50c in a straight line. Ship A is moving directly away from the Sun and ship B iscip8t(9. ysy q 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 dehecsh0t4 cqjqg60m:. 3x+j r ypends on the observer's frame 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 increvu:bbhem lm1+(1 (w bj3ooxj5ases, 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, rela),pab 8hf)nzstive to the shore, does it move isf)p,hb8 n) zan 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 what speed,dlzcm* a.i+ u; :gx 0ay4qr0ru relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat is heading downstrerdu iyx+zm04q c0 :a*r;alg .uam?

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 m/s in still water. Wit vmfzfc+, u uu6 ,do262f*civrh what speed, relative to the shore, does it move in a river that is flowing at 1.0 m/s if the boat 6orc*,d,6fm f zf2+i ucv2uuvis 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 travel if it is to be obs7r7ecvj0q99ilq fkl brv3 )o8erved by a stationary observer as running at one-half its normalcq) 8 0eq bi v37r9vfolr79jkl 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 nons ehu0o9glx(fc csl+* ij2lh;:top journey to a planet and returns in 10 hours according to a clock on the spaceship. If the speed of the spaceship is 0.80c, how much tis: j(i* clhu;9g0cll ehf+ 2xome 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 initially 10 years old. While Courtneh-1yo(l7 pz tujj2rvr ;.6rkoy remains on Earth, Andrea rides on a space ship whjvo ru lt po.j71rhrz2;( k6-yich travels away from Earth at a speed of 0.6c for five years (as measured by Courtney), then turns around and comes 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 takes a space trip with a speed of 0.8syj ,n:+t y;vh0c for 30 years according to a clock on the spaceship. Upon +:yvth,s n yj;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 ikxj v:)1;1 mmgm (dgowith 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 move to contract to halyqiroz-9s +q wn/l47hf of its proper length sqw+-q lh4n9izo /y7 r(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 space81vg2m)o:p3ipad3 v-y ef 5 4mjm gppkjqp6 j8ship is 10 m when it is at rest. If the spaceship travels by you with a speed of 0.70c, what length does it appea5j1mdfm 4-egp pav2 ppk3mv):6 jyp oq88gi 3jr 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 system is Alpha Centajy10pe80pv zjsu e7gr*d0p x(uri, 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 (x80 1ejv rpjzgd7ypesup* 0 0the 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 .67 femp7 qy (sjk igrr/)cg7tz8jsn- system is Alpha Centauri, which is 4.30 light years away. A spaceship with a constant speed of 0.800c relative /sn.fjk7q jrcpt7 e8gsg)riz7( my-6 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 Centauri, which is 4.30 3 4accm6.ny. w ks0wlnlight years away. A spaceship with a constant speed of 0.800c relative to the Earth travels toward the star. How much time would elapka 40.cm3w. lw6scnn yse 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 0.85c. What is its ma p,-s+x:lyenb9ln g 1wss? (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 rest massolwf cot)b:(sh1j2m 6?

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 your spaceship goes from 0.3 c to 0.6 ++r w;3bqid-( ixcjcb b1bks0c, then your mass will increasebr; c+(qb xs j3d+bii 10k-wbc 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 i n7u4:wg/jtt ifl8qg9uk /kp ;n $kg \cdot m/s$ 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 cnl/,7a qke18 m4eihqelement 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 bc 76y je)6 r (hzgwuuzkxoh9-8e released if 2.0 kg of material was lost during a reactiouokg 6-j9 uyh)ez(78 zxhrwc6n?

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(v 2a*lbagdr)dp4* duy pq9p9tna i,- is

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 Nagasaki in 1945 killed 140,000 peolhe1 gj77 )sxiple, helping to end World War II on the next day. It released energy equivalent to that of 20,000 tons of TNT explosive. How much mass was conve lg1) isjehx77rted 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. Wha3: e upt9zzhngn6d i24t is the speed of the pr4tz:zn32 gd9 he6niupoton?

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 8oukk36fhy2o2mugqrtx iv 4x - - z-9s10% of its total energy. What is the momentum -qxyxu--fuh124szkk6r to32g9m ivoin $kg \cdot m/s$ 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)x3n;h8lzkxk7f 3,shr o3lsj 0 during a reaction 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 durwb 6u cpx8/+sring 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 electron moving with a spm)h ptlirco89 27j9yzeed 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 acceleraerjkjxt:, huk+;l3 mv sw;j 4,g)nw.h23yhuate one kilogram of mass from rest ,e3h,)a:whgrt3u khwn 4l+j2y jkvmxj. u ;;sto a velocity 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, i*b n- zn; mmcts:20zba,mo/vs;c:ew$1017 J$ 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 through 100 kV. By what factor has its mso-q3nb9uu. 8dpx ssfo0g 8t7 ass increased wi o8t o7qusb gf.ups-dn830x9sth respect to its rest mass?

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 measure thzy5 0ya rsu ;xvup :y. d)ygcwhy.23q.e speed of li y3y).:.vu2p wayh.ux ry5ys0zdcq; gght from the Sun 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 traveling through space at 0.60 c relative to the Earth. c8wrhg/9 )i f8,dety t If the ships are headed directly toward each other, ft,8dhyt 8e/c r ig9)wwhat is their approach velocity, as measured by a person on 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. How fast would light t/,0gs2ok jzjq .yvw x0ravel from the headlights of j 0zw 2,/.svy0oxqkjgthe ship relative to a stationary observer?

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 spaceship tianr jl//(c 9rhen 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 ther(n/cr/j9al i Earth?

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 thej jfif)kbu 68q( a(em+r5 rn/y Earth with a speed of 0.80c. 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 th)j/ k(8i6ejryamfrn(uf5 q +be Earth if the missile 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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