Which planet has the same size but different masses, and no atmospheres?

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The discussion revolves around physics problems related to forces, motion, and gravitational effects on different celestial bodies. Participants analyze the frictional forces on a rotating merry-go-round, concluding that the friction exerted by the person is opposite in direction to that exerted on them. They also explore satellite speeds, determining that mass and radius influence orbital velocity, suggesting that a smaller radius with greater mass yields higher speed. Additionally, they examine the behavior of objects on two identical planets with different masses, noting that while the rate of free fall would differ, the mass balance and acceleration under a horizontal force would remain consistent. The conversation emphasizes the importance of understanding fundamental physics principles in solving these types of problems.
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When a person stands on rotating merry-go-round, the frictional force exerted on the person by the merry-go-round is:
a.greater in magnitude than the frictional force exerted on the merry-go-round by the person
b. opposite in direction to the frictional force exerted on the merry-go-round by the person
c. directed away from the center of the merry-go-round
d zero if the rate of rotation is constant
e. independent of the person's mass

I'm pretty sure it is b or c

2. Each of the five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each satellite are given below. Which satellite has the greatest speed?
Mass Radius
a. 1/2m R
b. m 1/2R
c. m R
d. m 2R
e. 2m R

I was thinking D because mv^2/r^2 is the equation so you want a big m and a small r to get the greatest v.

3. A ball attached to a string is whirled around at speed v in a horizontal circle having a radius r. if the radius of the circle is changed to 4R and the same centripetal force is applied by the string, the new speed of the ball is:
a. 1/4v
b. 1/2v
c. v
d. 2v
e. 4v

IDK how to even start this one mv^2/r^2 I'm thinking maybe 1/4 A
4. Two planets have the same size, but different masses, and no atmospheres. Which of the following would be the same for identical 1kg objects on the frictionless surfaces of the two planets?

I The rate at which each would fall freely
II The amount of mass each would balance on a double pan balance
III The amount of acceleration each would have when a certain horizontal force is applied

a. I only
b. III only
c. I and II only
d. II and III only
e. I, II, and III
 
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You MUST show relevant equations and an attempt at a solution.
 
alright
 
Sorry about not showing my thought process before but these are optional review problems that I would like to have done before my test Monday just to understand better.I do NOT have to hand them in.
 
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