Physics Question

[Opejay]

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I saw this question online ( Mcat question of the day). I tried solving it but I still don't understand how they arrived at the answer. I understand the fact that the mass does not change.

An object has a mass of 36 kg and weighs 360 N at the surface of the Earth. If this object is transported to an altitude equal to twice the Earth’s radius, then at this new elevated position the object will have:

A) Mass 4 kg and weight 40 N. (4%)

B) Mass 36 kg and weight 40 N. (17%)

C) Mass 9 kg and weight 90 N. (11%)

D) Mass 36 kg and weight 90 N. (68%)


The answer is B.

Thanks for your help.

 

[rjosh33]

I saw this question online ( Mcat question of the day). I tried solving it but I still don't understand how they arrived at the answer. I understand the fact that the mass does not change.

An object has a mass of 36 kg and weighs 360 N at the surface of the Earth. If this object is transported to an altitude equal to twice the Earth’s radius, then at this new elevated position the object will have:

A) Mass 4 kg and weight 40 N. (4%)

B) Mass 36 kg and weight 40 N. (17%)

C) Mass 9 kg and weight 90 N. (11%)

D) Mass 36 kg and weight 90 N. (68%)


The answer is B.

Thanks for your help.

Maybe I'm missing something, but I think they made a mistake. Formula for gravitational force is:

Fg = G(m1)(m2) / r^2

Holding everything in the numerator constant and doubling the radius results in multiplying the original force by 1/4. 360 x 1/4 = 90 N. I have no idea where they get 40 N from. That would be the right answer if the radius was tripled, not doubled.

 

[msamp]

Altitude is measured from the surface of the Earth not the center. So if the object is at an altitude 2x the radius its magnitude is 2x whatever the radius is. However, in the formula radius is from the center of the Earth, therefore while the object is 2 radii away from the surface, it is 3x away from the center. 3^2=9 so 360N/9= 40.

 

[qw098]

Maybe I'm missing something, but I think they made a mistake. Formula for gravitational force is:

Fg = G(m1)(m2) / r^2

Holding everything in the numerator constant and doubling the radius results in multiplying the original force by 1/4. 360 x 1/4 = 90 N. I have no idea where they get 40 N from. That would be the right answer if the radius was tripled, not doubled.

Yes, I chose D as well for the same reason as rjosh.

 

[btc8]

Maybe I'm missing something, but I think they made a mistake. Formula for gravitational force is:

Fg = G(m1)(m2) / r^2

Holding everything in the numerator constant and doubling the radius results in multiplying the original force by 1/4. 360 x 1/4 = 90 N. I have no idea where they get 40 N from. That would be the right answer if the radius was tripled, not doubled.

I initially thought that the answer was 90N as well, but I believe you have to account for the initial radius of the earth (r) and then ADD that to the final location (2r), so you get 3r.

Square three, you get 9, and then since you're increasing the radius, you decrease the force (F=1/r^2) by a factor of 9 which gives you get 40 N.

I could be wrong too, but this seems like one of those trick questions.

EDIT: What msamp said!

 

[rjosh33]

Altitude is measured from the surface of the Earth not the center. So if the object is at an altitude 2x the radius its magnitude is 2x whatever the radius is. However, in the formula radius is from the center of the Earth, therefore while the object is 2 radii away from the surface, it is 3x away from the center. 3^2=9 so 360N/9= 40.

Ah, yes, you're right. Altitude has its zero point at the surface.

Another question with contrived difficulty based on semantics. Those got pretty annoying in TBR.

 

[Singhp03]

Altitude is measured from the surface of the Earth not the center. So if the object is at an altitude 2x the radius its magnitude is 2x whatever the radius is. However, in the formula radius is from the center of the Earth, therefore while the object is 2 radii away from the surface, it is 3x away from the center. 3^2=9 so 360N/9= 40.

dudeeee good catch lol