Is my physics quiz on confirmations correct?

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SUMMARY

The physics quiz presented by the user includes three questions focusing on the concepts of center of mass, centripetal force, and conservation of angular momentum. The user selected answers B, B, and C for the respective questions. These answers are confirmed as correct: the center of mass may lie outside the object, the horizontal force on the ball points inwards, and bringing the hands closer to the chest increases rotational speed due to conservation of angular momentum.

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  • Understanding of center of mass in physics
  • Knowledge of centripetal force and its direction
  • Familiarity with angular momentum and its conservation
  • Basic principles of rotational motion
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CanadianEh
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Hi there, I have a multiple choice quiz that I completed for my physics class and I'm looking for confirmation on whether I'm correct or not.

1.The centre of mass of an object...
A. Must always lie outside the object, at a point where there is no mass.
B. May lie outside the object, at a point where no mass is.
C. Must always lie within the mass of the object



2. Consider a ball on the end of a string being whirled in a horizontal circle. The horizontal force acting on the ball points...
A. outwards, away from the centre of the circle
B. inwards, towards the centre of the circle
C. ... nonsense. There is no force at all on the ball



3. A man is standing on a turntable holding a dumbell in each of his outstretched hands. He is rotating at 1 rev/s. If he now brings his hands in close to his chest,
A. his rotational speed decreases
B. his rotational speed is unchanged
C. his rotational speed increases

The answers I got are B, B and C respectively. Can anyone confirm?
 
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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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