Question

Suppose a planet has twice the mass of the earth and twice the earth's radius. What is the acceleration of an object in free fall on this planet?
(Points : 3)
2.5 m/s2

4.9 m/s2

9.8 m/s2

4.9 × 106 m/s2

Answer 1

http://openstudy.com/#/updates/4f04a8fce4b075b56651dea6

Answer 2

What imran is saying is that. Let M be the mass of the earth, R its radius and m a mass falling on the earth, like a book or you. Then the force acting on the body m according to Newton's Universal Law of Gravitation is
\[ F = - \frac{GMm}{R^2} \]
as force = mass x acceleration, it must be that the acceleration on the body m is
\[ a_{earth} = - \frac{GM}{R^2} \]
This constant we usually write as g, and it is around 9.8 m/s^2.

Now what happens if the mass M doubles and R doubles? The new acceleration is
\[ a_{new} = - \frac{G(2M)}{(2R)^2} \]
Simplify that expression and write it as a multiple of \( a_{earth} = 9.8 m/s^2 \). Then you can find your answer.

Answer 3

Correction: What imran is saying is THIS....

Answer 4

net acceleration:
mg=GmM/R^2
g=GM/R^2
LET THE NEW ACCELERATION BE x
g/x=(GM*4R^2)/(R^2*2MG)
x=9.8/2=4.9m/s

Answer 5

salini: why give the answer completely when the method has been laid out? I prefer and recommend that we don't give the complete answer in such a case as this, because it gives the Questioner to learn more: they need to think through the problem more and complete the final steps themselves. Not only would they learn more, but they will also have the satisfaction of finding the answer themselves.

Answer 6

appreciate it, thank you for telling me.....