I heard that Jupiter is made out of gas. But in school I learned that Jupiter has gravity which is 2.5 times that of Earth (Gravity that can tear apart a comet) and gravity is proportional to mass.
So if Jupiter is made out of gas alone, how does it have such high gravity and maintain so many moons around it?
Comet Shoemaker–Levy 9 crashed into Jupiter a few years back.
As well as these molecules, emission from heavy atoms such as iron, magnesium and silicon was detected, with abundances consistent with what would be found in a cometary nucleus.
Those heavy elements are consistent with the comet being at least being partially composed of rock. So Jupiter is known to contain at least some rock. In fact, gas giants are thought to form around an initial small rocky or metallic core, which has sufficient gravity to draw in hydrogen, helium, water etc. from the protoplanetary nebula. By 'small rocky core' something with the mass of two or more earths is usually implied. The gravity field of such a body makes it difficult for even hydrogen to achieve escape velocity.
It doesn't matter if the body is made of gas, rocks, liquid or plasma, the four states of matter all have mass. So, as we know, mass create a gravitational field, and the more mass the stronger the gravity - and Jupiter has 317x Earth mass.
I concur with everyone else here (of course) that the gravity at the "surface" of Jupiter is entirely determined by the mass contained within that surface. The composition makes no difference.
However I differ with some on the answer to the headline title question. We simply do not know whether Jupiter has a rocky core.
A popular theory for the formation of giant planets is that they must begin by forming a rocky/icy core with perhaps a mass of 10-20 times the mass of the Earth. This then slowly accretes for a few million years until it grows massive enough for a runaway short period of gas accretion that builds its entire mass. See http://blog.planethunters.org/tag/core-accretion/ for another popular account.
If Jupiter formed like this then it should have a core. However, this is not the only game in town. Planets could also form in the protoplanetary disk by collapsing directly, in which case there would be no rocky/icy core. The recent discoveries of possible planet formation around the $<1$ million-year old HL Tau has led to a resurgence of this idea - it is difficult to form gas giants by core-accretion so quickly.
The answer may come reasonably soon. In July 2016, NASA's Juno spacecraft will arrive in orbit around Jupiter. One of its prime mission objective is to gather more information on how massive the core is at the centre of Jupiter using a battery of instruments including an experiment very sensitive to tiny gravitational field variations.
http://en.wikipedia.org/wiki/Juno_(spacecraft) http://www.nasa.gov/mission_pages/juno/overview/index.html#.VI9PuiusVSg
According to Newton's Law of Universal Gravitation, you simply need interacting masses in order to generate a gravitational force between them. Gases have mass and they therefore can contribute to gravity. So even if Jupiter is entirely gaseous, it is so incredibly massive besides (so much gas!), that it has a much stronger gravitational pull than Earth. The Sun is gaseous too, after all.
Be cautious, however, when someone compares gravitational forces so simply as "2.5 times". There is always a hidden assumption/reference in this because the force depends on more than just mass (e.g. distance). Earth's gravity is way stronger where I sit! In your teacher's case, it is probably meant that the gravitational force felt at the surface of Jupiter is 2.5 times what you would feel on the surface of Earth. To choose a "surface" for a gaseous planet, you need to make more assumptions.
Anyhow, for the titled question, it is highly likely that Jupiter is not entirely gaseous. With all of that matter (not just hydrogen and helium, but everything else everything in our solar system is made of) and all of that gravitational pull, you are bound to have precipitated solids that condense into a solid planetary core.
