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1) Two planets X and Y (sphere) both have 1 satelite revolving at low altitude about them. If the theri periods of rotation are found to be the same, which of the followings properties regarding X and Y is most likely to the the same?
A) Mass
B) Average density
C) Acceleration due to gravity at their surfaces
D) Radius
The answer is B. I don't know how this answer can be figured out.
My attempt before :
The centripetal force required for the satelite is provided by gravitation force
=> GMm / r 2 = mv2/ r
=> v= sqrt( GM / r)
Period = 2 (pi) r / v
= 2 (pi) sqrt ( r3 / GM)
Their period are the same=> 2 (pi) sqrt ( rx3 / GM)= 2 (pi) sqrt ( ry3
=> rx3 / M = ry3 / M
Thus I guess the answer to be D. How should be answer be deduced correctly by appropriate concepts?
2) Suppose there is a large spacecraft revolving about the earth. There are 2 people, A and B, of same mass in the spacecraft each approaching other in opposite direction. A is carrying a box. The question is, how can collision of A and B be prevented by A's throwing the box to B?
First of all, prior to going into the question, I think their speed should be different. Since A(with a box) and B have different mass, they have to have differecnt velocity so that they can still perform uniform circular motion. Is it right? Moreover, for B to be able to receive the box, A should throw the box with a range of velocity such that the box can perform uniform circular motion around more or less the same radius as that of B, right?
As A throws the box to B, some momentum is transferred to from A to B via the box, right? However, in this case, the principle of conservation of linear momentum does not hold, since there is external forces acting on the system ( A with a box together with B), which is the centripetal forces (or gravitation forces). Hence, I wonder if the above consideration can still be valid. If yes, why? If no, what should be considered?
If A and B are not to collide, after throwing the box, A should have reverse velocity with vA> VB. However, after thinking in deep, I guess that after throwing the box, the velocity of A changes. And A can no longer perform uniform circular motion, and so is B, right? Eventually A and B would hit the spacecraft . Would the velocity of the spacecraft be affected?
Thanks a lot to answer me such conceptual troublesome questions!
A) Mass
B) Average density
C) Acceleration due to gravity at their surfaces
D) Radius
The answer is B. I don't know how this answer can be figured out.
My attempt before :
The centripetal force required for the satelite is provided by gravitation force
=> GMm / r 2 = mv2/ r
=> v= sqrt( GM / r)
Period = 2 (pi) r / v
= 2 (pi) sqrt ( r3 / GM)
Their period are the same=> 2 (pi) sqrt ( rx3 / GM)= 2 (pi) sqrt ( ry3
=> rx3 / M = ry3 / M
Thus I guess the answer to be D. How should be answer be deduced correctly by appropriate concepts?
2) Suppose there is a large spacecraft revolving about the earth. There are 2 people, A and B, of same mass in the spacecraft each approaching other in opposite direction. A is carrying a box. The question is, how can collision of A and B be prevented by A's throwing the box to B?
First of all, prior to going into the question, I think their speed should be different. Since A(with a box) and B have different mass, they have to have differecnt velocity so that they can still perform uniform circular motion. Is it right? Moreover, for B to be able to receive the box, A should throw the box with a range of velocity such that the box can perform uniform circular motion around more or less the same radius as that of B, right?
As A throws the box to B, some momentum is transferred to from A to B via the box, right? However, in this case, the principle of conservation of linear momentum does not hold, since there is external forces acting on the system ( A with a box together with B), which is the centripetal forces (or gravitation forces). Hence, I wonder if the above consideration can still be valid. If yes, why? If no, what should be considered?
If A and B are not to collide, after throwing the box, A should have reverse velocity with vA> VB. However, after thinking in deep, I guess that after throwing the box, the velocity of A changes. And A can no longer perform uniform circular motion, and so is B, right? Eventually A and B would hit the spacecraft . Would the velocity of the spacecraft be affected?
Thanks a lot to answer me such conceptual troublesome questions!
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