All matter has gravity. But it takes a lot of matter to make a little bit of gravity. That is why in our normal lives, we only interact with the gravity of the earth, or if we are by the ocean, of the moon. But a big enough object has its own gravitational field. Just how big? Could a mountain have a gravitational field strong enough that something falling by it, like a raindrop, would be diverted from its course towards the earth and instead bend towards the mountain? It is an interesting question, and I am curious what people's initial guesses would be. Take a time, ponder the puzzle, and when you think you have an answer, read my solution.
To get an idea of the gravitational field of a mountain, I looked to the skies, specifically at Deimos, one of Mars irregular moons. According to NASA, Deimos has a surface gravity of 0.003 meters a second, meaning an object at its surface (or just above it) would move downwards at 0.003 meters per second, with its velocity increasing steadily with each passing second. This is very weak compared to earth's gravity, which is 9.8 meters per second. Deimos has a size of around 6.2 kilometers, or about 20,000 feet tall. Deimos is less dense than a mountain, with many astronomers believing it is a barely-consolidated bunch of gravel and rubble rather than a solid rock. Deimos mass might be roughly equal to a mountain 5,000 feet tall. And on Earth, we do have mountains with sheer drops of close to a mile: Mount Thor in Baffin Island, for example, has a sheer drop of 4000 feet. We can thus estimate that a raindrop falling parallel to the surface of Mount Thor, would feel about as much gravity from the mountain as if it was on the surface of Deimos.
Three millimeters per second is not a microscopic change in velocity. After ten seconds of fall, it would be moving at 3 centimeters a second towards the mountain. At least some of those raindrops should bend towards the mountain, and hit it.
The problem is with terminal velocity. Especially with something as small as a raindrop, the resistance and friction of air would quickly slow it down. Smaller raindrops can almost hover in air against the pull of the earth's gravity, let alone the measly gravity of a mountain. And in comparison to other forces: wind turbulence or even electrical repulsion or attraction, the gravity of the mountain would disappear. So even though the gravity of a mountain is theoretically strong enough to bend raindrops towards it, it would take an incredibly specific set of circumstances (a single drop of water falling parallel to a sheer cliff on a very tall mountain, on a totally windless day) for it to be something that could be practically measured.
At least, that is my answer...what is yours?