Question

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.

Answer 1

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

`F=G (m M)/(r^2)`
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:

`F= M a_M`

`F= m a_m`
So the accelerations of the two objects are:

`a_M = (F)/(M)`

`a_M = (F)/(m)`

we can see from the two equations that
1) the acceleration of the massive object,
`a_M`, is very small because its mass M is big
2) the acceleration of the less-massive object,
`a_m`, 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)