Physics TPR question

[piojita63]

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Hello forum!
I am doing the TPR online drills that come with the review books.
I am not the best at physics, so I am working very hard to gain a conceptual understanding of the topics. Anyway, I just read the explanation to this question and it simply doesn't make sense to me. Can anyone explain it to me? I really appreciate your time with this.

If an animal were transported to a planet made up of the same material as Earth, but with twice its radius, how would the animal’s weight be affected?


A.
It would weigh one fourth as much as on Earth.


B.
It would weigh half as much as on Earth


C.
It would weigh the same as on Earth.


D.
It would weigh twice as much as on Earth.



This is my logic (which is wrong, according to TPR): Since weight (mg) is inversely proportional to r2 (r squared), if r is doubled, that means that weight is now LESS than before (by a factor of 4, since 2 squared is 4). Thus, to me the answer should be A. However, TPR says that the answer is D and I really don't understand their explanation.
Can someone please correct my logic and explain why it is D in their own words? Why am I wrong?

 

[aspiringdoc09]

Hello forum!
I am doing the TPR online drills that come with the review books.
I am not the best at physics, so I am working very hard to gain a conceptual understanding of the topics. Anyway, I just read the explanation to this question and it simply doesn't make sense to me. Can anyone explain it to me? I really appreciate your time with this.

If an animal were transported to a planet made up of the same material as Earth, but with twice its radius, how would the animal's weight be affected?


A.
It would weigh one fourth as much as on Earth.


B.
It would weigh half as much as on Earth


C.
It would weigh the same as on Earth.


D.
It would weigh twice as much as on Earth.



This is my logic (which is wrong, according to TPR): Since weight (mg) is inversely proportional to r2 (r squared), if r is doubled, that means that weight is now LESS than before (by a factor of 4, since 2 squared is 4). Thus, to me the answer should be A. However, TPR says that the answer is D and I really don't understand their explanation.
Can someone please correct my logic and explain why it is D in their own words? Why am I wrong?

I am using the same logic as you, and would get the same answer. Weight (=mg) is a force and you will set it equal to Newton's Law of Gravitation (F=GMm/r^2), which is also a force. If you set the two equal, then it is clear that W is inversely proportional to r^2. Therefore, if you double the radius, you decrease the weight by 4.

I believe it is a mistake.

 

[chiddler]

You double the radius, then mass increases, too.

So 2x radius gives you how much more volume? v = 4/3*pi*r^3. Two times radius gives 2^3 volume = 8.

F = GmM/r^2

M is increasing by 8. R is increasing by 4. 8/4 = 2 times more gravity.

I think what sucks about this question is that you get SO MANY "increase radius without increasing mass" questions in practice tests that realizing mass will increase becomes difficult. I'm glad you posted it because I made the same mistake.

 

[aspiringdoc09]

You double the radius, then mass increases, too.

So 2x radius gives you how much more volume? v = 4/3*pi*r^3. Two times radius gives 2^3 volume = 8.

F = GmM/r^2

M is increasing by 8. R is increasing by 4. 8/4 = 2 times more gravity.

I think what sucks about this question is that you get SO MANY "increase radius without increasing mass" questions in practice tests that realizing mass will increase becomes difficult. I'm glad you posted it because I made the same mistake.

I'm glad the OP posted this too because 10/10, I would have missed this question. I didn't think the mass (M) would be affected, but I guess it makes sense. However, the volume equation for sphere's was far from my mind, but if you increase radius you would have to increase the volume. They sure know how to make an easy question difficult. You're right, they usually don't ask this question type. Thanks OP and chiddler.👍

 

[piojita63]

You double the radius, then mass increases, too.

So 2x radius gives you how much more volume? v = 4/3*pi*r^3. Two times radius gives 2^3 volume = 8.

F = GmM/r^2

M is increasing by 8. R is increasing by 4. 8/4 = 2 times more gravity.

I think what sucks about this question is that you get SO MANY "increase radius without increasing mass" questions in practice tests that realizing mass will increase becomes difficult. I'm glad you posted it because I made the same mistake.

WOW!!! 😱 Incredible. Thank you sooo much! I didn't even know (or remember) that the volume of a sphere is equal to 4/3pi*r^3....Do I really need to know a bunch of weird volume formulas for different shapes for the MCAT?
You are right...we get used to these "increase radius without increasing mass", so we didn't take into account the fact that mass is proportional to volume when calculating.
Wow TPR...thanks for making me feel even worse about my physics ability. 🙁

I was just about to give up and think it was a mistake too!

 

[syoung]

You double the radius, then mass increases, too.

So 2x radius gives you how much more volume? v = 4/3*pi*r^3. Two times radius gives 2^3 volume = 8.

F = GmM/r^2

M is increasing by 8. R is increasing by 4. 8/4 = 2 times more gravity.

I think what sucks about this question is that you get SO MANY "increase radius without increasing mass" questions in practice tests that realizing mass will increase becomes difficult. I'm glad you posted it because I made the same mistake.

We can assume that mass increases with the radius because it says the planet is made up of the same "stuff" ie density? so therefore d=m/V so if same d then if V goes up by 8x, m goes up by 8x and so therefore: F=GMm/r^2 --> 8/4 = 2 yes?

 

[piojita63]

We can assume that mass increases with the radius because it says the planet is made up of the same "stuff" ie density? so therefore d=m/V so if same d then if V goes up by 8x, m goes up by 8x and so therefore: F=GMm/r^2 --> 8/4 = 2 yes?

Yes, that is what I gathered from the poster above. W is proportional to 8/4 (8 from the mass, derived from the volume of a sphere equation and 4 from the squaring of the radius)=2/1.

Crazy question TPR!!!!

You are very welcome that I posted it! I was even regretting it for a bit, thinking I would get bashed for my physics stupidity. It's glad to know that there are positive people out there willing to help one another this way! Best of luck to all with this studying!

 

[aspiringdoc09]

Yes, that is what I gathered from the poster above. W is proportional to 8/4 (8 from the mass, derived from the volume of a sphere equation and 4 from the squaring of the radius)=2/1.

Crazy question TPR!!!!

You are very welcome that I posted it! I was even regretting it for a bit, thinking I would get bashed for my physics stupidity. It's glad to know that there are positive people out there willing to help one another this way! Best of luck to all with this studying!

Don't feel bad about the physics. It's my worst subject. I use to think orgo was bad but I am better at understanding that once I focus on vs physics. I can't seem to understand physics fully no matter what I do. It is definitely my KRYPTONITE! Good luck OP.

 

[Class1P]

Don't feel bad, this is a very tricky question. I said the same as you until somebody pointed out that the mass wasn't staying the same.

If you double the radius you increase the volume of a sphere by a factor of 8 and thus the material it is made out of and its mass.