宇宙中存在一些质量相等且离其他恒星较远的四颗星组成的四星系统_爱下问搜题

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问题多选题

宇宙中存在一些质量相等且离其他恒星较远的四颗星组成的四星系统，通常可忽略其他星体对它们的引力作用．设四星系统中每个星体的质量均为m，半径均为R，四颗星稳定分布在边长为a的正方形的四个顶点上．已知引力常量为G．关于四星系统，下列说法错误的是（忽略星体自转）（　　）

A．四颗星围绕正方形对角线的交点做匀速圆周运动

B．四颗星的轨道半径均为

a

2

C．四颗星表面的重力加速度均为G

m

R2

D．四颗星的周期均为2πa

2a

(4+

2)Gm

答案

A、星体在其他三个星体的万有引力作用下，合力方向指向对角线的交点，围绕正方形对角线的交点做匀速圆周运动，故A正确．

B、四颗星的轨道半径为r=

2

2

a．故B错误．

C、根据万有引力等于重力有：G

mm′

R2

=m′g，则g=

Gm

R2

．故C正确．

D、根据万有引力提供向心力G

m2

(

2

a)2

+2G

m2

a2

cos45°=m

2

2

a(

2π

T

)2，解得T=2π

2a

(4+

2

)Gm

．故D错误．

本题选错误的，故选BD．

完形填空

When Dave was eighteen, he bought a secondhand car for 200 so that he could travel to and from work more____ than by bus. It worked quite well for a few years, but then it got so old, and it was costing him __much in repairs that he decided that he had better __it.
　　He asked among his friends to see if anyone was particularly_ _ to buy a cheap car, but they all knew that it was falling to pieces, so__ of them had any desire to buy it. Dave's friend Sam saw that he was __ when they met one evening, and said, “What's __, Dave?”
　　Dave told him, and Sam answered, “Well, what about advertising it in the paper? You may __more for it that way than the cost of the advertisement!” Thinking that Sam's__was sensible(合理的),he put an advertisement in an evening paper, which read “For sale: small car, __ very little petrol, only two owners. Bargain at 50.”
　　For two days after the advertisement first appeared, there was no __.But then on Saturday evening he had an enquiry(询问).A man rang up and said he would like to__ him about the car. “All right,” Dave said, feeling happy. He asked the man whether ten o'clock the next morning would be__or not. “Fine,” the man said, “and I'll __my wife. We intend to go for a ride in it to __ it.”
　　The next morning, at a quarter to ten, Dave parked the car in the square outside his front door, __ to wait there for the people who had__ his advertisement. Even Dave had to __that the car really looked like a wreck(残骸).Then, soon after he had got the car as clean__ it could be, a police car stopped just behind him and a policeman got out. He looked at Dave's car and then said, “Have you reported this __ to us yet, sir?”?

D．astonished?

D．description?

单项选择题

下列关于维生素C结构和性质的叙述，那一项是错误的：（）

A.维生素C是一种内酯化合物

B.维生素C具有酸性是因为-COOH释放质子

C.还原型维生素C为烯醇式，而氧化型维生素C为酮式

D.人缺乏时会产生坏血病