Identical objects carry a net charge

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Two identical conducting objects initially carry net charges, with one attracted to a positively charged ebonite rod and the other repelled. After touching, both objects are repelled by the rod, indicating they must both have the same charge after contact. The conclusion is that one object was initially positive and the other negative, with the positive charge having a greater magnitude than the negative. If the objects were insulating, the charge distribution would differ, affecting their interactions with the rod. The final conclusion is that the initial charge configuration led to both objects being positively charged after contact.
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Homework Statement


Each of the two identical objects carry a net charge. The objects are made of conducting material. One of them is attracted to a positively charged ebonite rod, and the other is repelled by the rod. After the objects are touched together, it is found that they are each repelled by the rod. What can be concluded about the initial charges on the objects?

a) initially, both objects are positive, with both charges having the same magnitude.
b) Initially both objects are negative, with both charges having the same magnitude.
c) Initially one object is positive and one is negative, with the positive charge having a greater magnitude than the negative charge.
d) Initially one object is positive and one is negative, with the negative charge having a greater magnitude than the positive charge.

Homework Equations


E(r)=k*Q/r^2

F=k*lQ1l * lQ2l / r^2 [the bars are supposed to represent the magnitude]


The Attempt at a Solution


The answer is c). Could you please explain thoroughly (but in simple words if possible) why that is the case, and why it's the positive charge that has to have a greater magnitude and not the negative?
Also, what difference would it make if the objects were made of insulating material?
 
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You know that they are of opposite charges, since one is attracted to the rod and the other is repelled. After touching, they are both repelled, so that means both are positive in the end. Since they were of opposite charges to start, the positive charge has to "win" over negative during the transfer.
 
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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