I was just studying meteorology and had a doubt about the motion of meteors towards earth.
Can a meteor be stopped while it is still under under the gravitational influence of Earth? As far as I know some meteors are very bulky and their motion towards the Earth's surface is with a huge magnitude of momentum. Has any organisation made any equipment to stop these meteors?
Two terminology issues first.
First, cosmology is the study of how the universe began and what will ultimately happen to it. Pieces of rock in our solar system have nothing to do with cosmology.
Second, a meteoroid is a small solid body in the solar system. A meteor is what we call such a body while it is falling through our atmosphere, usually glowing hot (e.g. a "shooting star"). When it hits the ground, whatever is left is called a meteorite.
Now to answer the underlying question. You have to understand that meteoroids come in every size from grains of sand to kilometers across. If something on the large end were headed toward us, there is little we could do without advanced preparation. That said, the larger the rock, the easier it is to detect, and thus the more warning we might hope to have. Gently pushing on a meteoroid for a long time can change it's orbit plenty in order to avoid hitting the Earth. There's no reason you would try to stop it's motion entirely; just nudge it out of the way. And for smaller objects, they will simply burn up in the atmosphere.
As of right now we have no way of deflecting an asteroid on its way to hitting the Earth. However there are lots of organisations tasked with looking into the issue. The Wikipedia article on Asteroid impact avoidance would be a good place to start. Also see the NASA Near Earth Orbit site for lots more background.
You are quite correct than the kinetic energy of an asteroid comparable to the one that wiped out the dinosaurs is enormous, and we have no chance of stopping it directly. However if we spot the asteroid early enough we can try and push it sideways to change its orbit. On the scale of the Solar System the Earth is a very small target, so if you can change the orbit of an asteroid by even a small amount that may be enough to make it miss the Earth.
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Can a meteor be stopped while it is still under under the gravitational influence of Earth?
you mean in the final stages of the asteroid's approach to Earth, then no if we leave it that late we are all doomed to follow the dinosaurs. If you allow a more liberal interpretation, note that many near Earth objects will fly by the Earth several times before eventually hitting it. On each flyby the Earth's gravity changes the orbit a bit until finally the change results in an impact. We might be able to deflect the asteroid during a flyby and make a big enough change to stop it hitting the Earth in the future.
It's hard to predict the orbit of an asteroid more than a few orbits in advance, because even tiny effects can add up to large changes in the orbit. So while we could possibly avoid an impact predicted for the next flyby, or the one after that, it's hard to be sure what would happen to the asteroid in the far distant future. Hopefully if we can gain a century or two our technology will have advanced enough in that time to make the next potential impact easier to deal with.
