# What is the magnitude of acceleration?

#### YMMMA

1. Homework Statement
Objects X and Y, shown below, are released fronm rest in outer space. The only force acting on the objects is their mutual gravitational attraction. The mass of X is one-half that of Y. With respect to the original rest frame, the magnitude of the acceleration of X is

(A) one-half that of Y
B) twice that of Y
C) equal to that of Y
D) directly proportional to the distance betweern X and Y
(E) directly proportional to the square of the distance between X and Y

2. Homework Equations
Gravitational force Fg = GXY/r^2, r is the distance between the two masses.
Fnet=ma

3. The Attempt at a Solution
Using both equations, Xa=GXY/r^2. Acceleration of X is Simplified to a=GY/r2. And Ya= GX/r^2 simplified to a=GX/r^2= acceleration of Y. Substituting X=½Y
So the ratio if acceleration of X to that of Y would be twice as much,B. Is there something wrong?

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#### YMMMA

What makes you think so?
Because in the answer key it is C, the same, so I had to check

#### haruspex

Homework Helper
Gold Member
2018 Award
Because in the answer key it is C, the same, so I had to check
Ouch. Does this text have many such blunders?

#### YMMMA

Probably yes. That’s a different book though.

#### SammyS

Staff Emeritus
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Because in the answer key it is C, the same, so I had to check
What is the same is:
The magnitude of force X exerts on Y is the same as the magnitude of force Y exerts on X .

Since the (magnitudes of the) forces are equal, the acceleration of each is inversely proportional to its mass → B is correct.

#### YMMMA

What is the same is:
The magnitude of force X exerts on Y is the same as the magnitude of force Y exerts on X .

Since the (magnitudes of the) forces are equal, the acceleration of each is inversely proportional to its mass → B is correct.
Yes, thank you!

"What is the magnitude of acceleration?"

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