I have this problem that I really don't get. It goes like this:
"Rex weighs 200 pounds on the surface of a planet that has the same radius as Earth but four times its mass. How much would Rex weigh on a planet that has the same mass as Earth but half its radius?"
A) 50 lbs B) 100 lbs C) 200 lbs D) 400 lbs E) 800 lbs
The formula you have to use is W = (Gm)/r^2
G= universal gravitational constant
W = weight, or force of gravity on the mass
m = mass
r ^2= radius squared
The answer is 200 lbs, but I don't get why. I tried using the formula and it doesn't work. Can anyone explain please????
2007-10-28 22:00:01 · 5 answers · asked by Exotic traveler 4 in Science & Mathematics ➔ Astronomy & Space
Weight is directly proportional to mass and inversely proportional to the square of the radius. If you represent a person's weight on Earth as W, then if the radius is unchanged but the mass of Earth is increased four times his weight becomes 4xW. If the mass is unchanged but the radius is reduced by 0.5 then his weight becomes 1/0.5^2 xW. 1/0.5^2 = 1/0.25 = 4, so his weight is 4xW, or the same as on a planet four times the mass of Earth with the same radius.
2007-10-28 22:16:11 · answer #1 · answered by Jason T 7 · 1⤊ 0⤋
Suppose the mass of earth = E ,and mass of the first planet is P and radius of the earth is R. Then, Weight on the first planet is given by
G E P /R^2
or
G E (4E)/R^2
or
4GE^2/R^2
Now consider the second planet whose radius is half of the earth's radius in this case the weight is given by
G E P/(R/2)^2
or
GEE/ (R^2/ 4)
or
4GE^2/R^2
So you can see that the wight calculated in both the cases is same. Hence it will be 200lbs only on both the planets
2007-10-28 22:18:46 · answer #2 · answered by s_sanjay9 5 · 0⤊ 0⤋
The mass is x 4, but the radius halves. But you use the square of the radius, which is one quater, these cancel which means the weight is the same 200 pounds.
2007-10-28 22:11:51 · answer #3 · answered by Steve 2 · 0⤊ 0⤋
On the first planet, using the given formula , we can say that,
W=200lbs
=>200=Gm/r^2
=>200=G(4m)/r^2
=4Gm/r^2-i
On the second planet,
r=r/2
m=m
We know
W=Gm/r^2
=Gm/(r/2)^2
=Gm/r^2/4
=4Gm/r^2
However, From i, we know,
4Gm/r^2=200lbs.
Thus , the answer is 200lbs, just like you said.
2007-10-28 22:25:32 · answer #4 · answered by Anonymous · 0⤊ 0⤋
Before I try this on paper, are you remembering that r is the distance between the two centres of gravity? Sorry if I'm insulting your intelligence.
2007-10-28 22:06:32 · answer #5 · answered by Anonymous · 0⤊ 0⤋