TBR CBT #2 Q8 - center of mass

[brood910]

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8.Given M2 > M1, which of the following pendulum systems has the GREATEST change in potential energy from a state of rest?

In the passage, it states that greatest PE = center of mass is more displaced away from its resting state.

D is the best answer. Choices A and C can be eliminated immediately, because both of them depict systems in which only one of the two balls is displaced. In choice B (System I), the center of mass when the system is at rest is lower than for choice D (System II), so that point is displaced by a greater distance when System I is moved by the same angular amount as System II. The greater the displacement of the center of mass, the greater the change in the potential energy of the system. The best answer is D.

I am kinda confused here.
If B has center of mass at LOWER point, doesnt it displace away from its resting state by greater change in height?

Also, I thought the center of mass is lower for D, not B, because the lowest ball is heavier.
In the answer explanation for another question, it says "The center of mass for the two balls must be closer to the lower ball." (pic below)

 

[IlyaR]

I'm about 1 month out from studying (Jan 23rd exam) so keep that in mind. The way that I did it was (as TBR mentions) eliminating A and C, then comparing B and D. I figured that since both points have to swing 45 degrees, intuitively the end of the pendelum would displace more height. (Think about the anchor point, it would also swing 45 degrees but would not change in height at all). Then just think of PE=mgh. D makes the most sense

 

[brood910]

I'm about 1 month out from studying (Jan 23rd exam) so keep that in mind. The way that I did it was (as TBR mentions) eliminating A and C, then comparing B and D. I figured that since both points have to swing 45 degrees, intuitively the end of the pendelum would displace more height. (Think about the anchor point, it would also swing 45 degrees but would not change in height at all). Then just think of PE=mgh. D makes the most sense

Thanks for the response, but you technically repeated what I said.
That was my reasoning as well. Like you said, lower point will displace more height.

If B has center of mass at lower point, then if what we are saying is true, B must be the answer, not D.

I think their answer explanation is wrong because B actually has center of mass at higher point. Then, it makes sense why D is the answer.

 

[IlyaR]

In choice B (System I), the center of mass when the system is at rest is lower than for choice D

If this is what you are referring to, they mean the magnitude, not the actual position of the center of mass


edit: disregard that, I think they just messed up the explanation

 

[brood910]

If this is what you are referring to, they mean the magnitude, not the actual position of the center of mass


edit: disregard that, I think they just messed up the explanation

Yep..
They seriously should improve their CBT system as well. Their questions are great, but the system itself is so baddddd like their website..

 

[scrub2scrubs]

I agree, I think B is the right answer as well. I didn't really solve it using center of mass, but I just tried to calculate what the PE of each system would be. Since M2 is at a larger height, the overall system would have a higher potential energy.

 

[brood910]

I agree, I think B is the right answer as well. I didn't really solve it using center of mass, but I just tried to calculate what the PE of each system would be. Since M2 is at a larger height, the overall system would have a higher potential energy.

No. Their answer is correct. It's D.
It's just their explanation that they messed up. D has lower center of mass, but they said B has lower center of mass.

 

[scrub2scrubs]

Oh I see lol. I guess my reasoning didnt make sense