问题 选择题

宇宙飞船在宇宙深处飞行的过程中,发现A、B两颗均匀球形天体,两天体各有一颗靠近其表面飞行的卫星,测得两颗卫星的周期相等,以下判断正确的是(  )

A.两颗卫星的线速度一定相等

B.天体A、B的质量一定不相等

C.天体A、B的密度一定不相等

D.天体A、B表面的重力加速度之比等于它们的半径之比

答案

A、设A、B中任意一个球形天体的半径为R,质量为M,其卫星的质量为m,周期为T.

卫星的线速度为:v=

2πR
T
,T相等,而R不一定相等,线速度不一定相等.故A错误.

B、由题意,卫星靠近天体表面飞行,卫星的轨道半径约等于球形天体的半径,则有:

G

Mm
R2
=m
4π2
T2
R,

得:M=

R3
GT2
,T相等,R不一定相等,所以天体A、B的质量不一定相等.故B错误.

C、天体的密度为ρ=

M
V
=
R3
GT2
4
3
πR3
=
GT2
,可见,ρ与天体的半径无关,由于两颗卫星的周期相等,则天体A、B的密度一定相等.故C错误.

D、天体A、B表面的重力加速度等于卫星的向心加速度,即g=a=

4π2R
T2
,可见天体A、B表面的重力加速度之比等于它们的半径之比,故D正确.

故选:D

多项选择题
阅读理解

When I was six, Dad brought home a dog one day, who was called “Brownie”. My brothers and I all loved Brownie and did different things with her. One of us would walk her, another would feed her, then there were baths, playing catch and many other games, Brownie, in return. loved each and every one of us. One thing that most touched my heart was that she would go to whoever was sick and just be with them .We always felt better when she was around.

One day, as I was getting her food, she chewed up(咬破)one of Dad’s shoes, which had to be thrown away in the end. I knew Dad would be mad and I had to let her know what she did was wrong. When I looked at her and said, ”Bad girl,” she looked down at the ground and then went and hid. I saw a tear in her eyes.

Brownie turned out to be more than just our family pet, she went everywhere with us .People would stop and ask if they could pet her. Of course she’d let anyone pet her. She was just the most lovable dog. There were many times when we’d be out walking and a small child would come over and pull on her hair. she never barked(吠) or tried to get away. Funny thing is she would smile. This frightened people because they thought she was showing her teeth. Far from the truth, she lovely everyone.

Now many years have passed since Brownie died of old age. I still miss days when she was with us.

小题1:What would Brownie do when someone was ill in the family?

A.Look at them sadly.

B.Touch them gently.

C.Play games with them.

D.Keep them company.小题2:We can infer from Paragraph 2 that Brownie__________.

A.world eat anything when hungry

B.felt sorry for her mistake

C.loved playing hide-and-seek

D.disliked the author’s dad