contestada

For two objects in space with very different masses, the gravitational force causes:

A. a large linear acceleration of the more-massive object.

B. no acceleration since the forces are equal and opposite.

C. only the smaller object to accelerate.

D. a net acceleration for the less-massive object.

Respuesta :

skyluke89
The correct answer is D.

In fact, the gravitational force exerted by the massive object on the less-massive object is equal to the force exerted by the less-massive object on the massive object, and it is equal to
[tex]F=G \frac{m M}{r^2} [/tex]
where m is the mass of the less massive object, M the mass of the massive object, G the gravitational constant and r the distance between the two objects.

For Newton's second law, the force acting on each of the objects is the mass of the object times its acceleration:
[tex]F= M a_M[/tex]
[tex]F= m a_m[/tex]
So the accelerations of the two objects are:
[tex]a_M = \frac{F}{M} [/tex]
[tex]a_M = \frac{F}{m} [/tex]

we can see from the two equations that
1) the acceleration of the massive object, [tex]a_M[/tex], is very small because its mass M is big
2) the acceleration of the less-massive object, [tex]a_m[/tex], is larger because its mass m is smaller

Therefore there will be a net acceleration produced on the less-massive object (and on the massive object, but it will be negligible)

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