How noticeable is the gravitational pull of a mountain range? A massive object like a planet exerts a great gravitational pull on nearby objects. This will cause them to accelerate towards the center of the planet with the same acceleration regardless of their mass, if we disregard other forces such as air resistance.
How does objects "connect"?
Mountain ranges are of great mass, and I assume they exert a gravitational pull of some degree. If you could theoretically "lift" this mountain range of the face of the planet by as little as 1 meter, would objects then get attracted to it enough for us to physically feel it? If not, would it help to place this mountain in space so that the pull of the earth wouldn't counteract the mountain effect?
 A: The effect is noticeable even here on Earth, and in fact it has been used to measure the mean density of the Earth in experiments such as the Schiehallion experiment. 
The principle is simple: take a pendulum. If there is no large-mass object nearby (such as a mountain), it will hang straight downward, pointing to the center of the planet. But if there is a large-mass object nearby it will pull the pendulum out of true.

In fact, with a sensitive enough instrument, it is possible to measure the gravitational pull of much smaller objects. In 1798 Henry Cavendish used a torsion balance to measured the gravitational attraction between balls of lead.
In space, the effect would of course be much greater because the predominant gravitational field of Earth wouldn't be there.
Update: clarification
I was quite sloppy with my last sentence, as CuriousOne correctly pointed out. Here's what I meant:
If you were able to detach the whole mountain from the surface of the planet and take it far from the planet itself, as it seems you are suggesting when you talk about "lifting" the mountain, the effect -the deflection of the pendulum- would indeed be greater. In fact, the gravitational pull exerted by the planet is proportional to $r^{-2}$, where $r$ is the distance from the planet's center. Since the deflection of the pendulum is (see here)
$$\theta = \arctan \left(\frac {F_M} {F_E}\right)$$
where $F_M$ is the force exerted by the mountain and ${F_E}$ the force exerted by the Earth, you can see that in this case the deflection would be greater.
If you took the mountain an infinite distance away from the planet (into deep space), the deflection would be  entirely due to the mountain and you would of course have $\theta = \pi/2$ (the pendulum would point towards the mountain's center of gravity).
