You travel to an unkown planet and carry out an experiment to determine the value of gravity. You Find it to be 19.6m/s2. This means that: Earths gravity is (9.8m/s2)

a) The planet has twice the mass of Earth.
b) The planet has half the mass of the Earth.
c) The planet has one half the radius of the Earth.
d) Both b) and c) are correct.

I was thinking a).

Thanks.
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Well it has a greater gravity force (an object would fall twice as fast). So I think it'd be A. I could be wrong though, haven't had a physic's class in like 4 years
yep A.

Newton's law of gravitation is Gm1m2/r^2=m1g assuming you're measuring with an object of mass M1.

It also means that the object (say a tennis ball) is exerting twice gravitational force on the planet than it exerts on earth. Yep, true story....
14 year old geometry student here, also suggesting A.
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It's d.

Bear with me. Remember, force is directionally proportional to mass, but INVERSLY proportional to the SQUARE of it's radius..

Have you seen the following formula before?

F = (MmG)r^2

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Last edited by LordBishek at Oct 22, 2008,
Quote by LordBishek
It's d.

Bear with me. Remember, force is directionally proportional to mass, but INVERSLY proportional to the SQUARE of it's radius..

Have you seen the following formula before?

F = (MmG)r^2

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its A

Quote by LordBishek
It's d.

Bear with me. Remember, force is directionally proportional to mass, but INVERSLY proportional to the SQUARE of it's radius..

Have you seen the following formula before?

F = (MmG)r^2

So it's have to have to same mass, but half the radius for it to have twice the gravitational force.
^ No, same mass, half radius would result in 4 times the gravitational force. (R/2)^2= R/4 which is on the bottom therefore 4 on top.
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Quote by Freddedonna
So it's have to have to same mass, but half the radius for it to have twice the gravitational force.

No, it needs to have HALF the mass, but HALF the radius to have TWICE the same gravitational force. I know it seems counter intuitive, but bear with me, I'll explain all in this proof, which I'm writing specially for TS.

To get the same force, you need to have half the radius, and A QUARTER of the mass.
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Quote by sk8boardbob2
^ No, same mass, half radius would result in 4 times the gravitational force. (R/2)^2= R/4 which is on the bottom therefore 4 on top.

Let's say R = 10

(10/2)^2 = 25
10/4 = 2.5

25 =/= 2.5
More mass=greater gravity. As has already been stated, a)
My bad. The right side of the equation should say (R^2)/4. That way (10^2)=100/4=25
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Quote by LordBishek

No, it needs to have HALF the mass, but HALF the radius to have TWICE the same gravitational force. I know it seems counter intuitive, but bear with me, I'll explain all in this proof, which I'm writing specially for TS.

To get the same force, you need to have half the radius, and A QUARTER of the mass.

this is certainly correct but multiplying one of the masses by a factor of 2 increases the gravitational force by a factor of 2 as well. It's the law of gravitation.

If you're decreasing both the radius AND mass of hte planet, however no where in the problem did it state that the radius was changed.
Fg = m*g =G* m*M/r^2

g =G* M/r^2

if g=19.6m/s/s that means that either the mass is twice as much as earth's or that the mass is the same and that the radius is 1.414 times larger
Document1.pdf EDITED AND CORRECTED

EDIT:

Shit, I've contradicted myself in there. The last page is fine, but I need to do some quick editing, so don't worry if it doesn't entirely make sense just yet, it will.
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Last edited by LordBishek at Oct 22, 2008,
i vote D

reasoning: A is too obvious

edit: well hello there mr. sciency lawd bishop, aren't you special? (actually that was an interesting read)

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Last edited by MTVget0FFtheAIR at Oct 22, 2008,
LordBishek, your simplified equation also holds true when you make the mass of planet Zugbop twice Earth's and ignore the radius. Therefore the answer to the question is a and d.
Last edited by kiwi68 at Oct 22, 2008,
Well.. gravity = mass * acceleration, so I'm guessing the mass of that planet is double that of Earth's.
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Quote by kiwi68
LordBishek, your simplified equation also holds true when you just double the mass of planet Zugbop. Therefore the answer to the question is a and d. TS's teacher needs to look more closely at their answers.

Yep.

And I got you to call it Zugbop
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Last edited by LordBishek at Oct 22, 2008,
^ The problem is answer D makes it sound like both B and C are correct individually, not when both occur which is what you did.
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Quote by sk8boardbob2
^ The problem is answer D makes it sound like both B and C are correct individually, not when both occur which is what you did.

No, because putting b) and c) down individually implies the wording (in a logic statement)

b (AND) c
Not b (exclusive OR) c

Also, teachers USUALLY don't put down answers like d) which reference 2 previous answers unless they're correct. I suppose covering your ass by putting down a) OR d) would work.
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