What is the magnitude of acceleration?

[YMMMA]

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

Homework Equations

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

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?

 

[haruspex]

. Is there something wrong

What makes you think so?

 

[YMMMA]

What makes you think so?

Because in the answer key it is C, the same, so I had to check

 

[haruspex]

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]

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!