Is the gravitational pull of Sun on moon greater than the gravitational pull that Earth has over moon?
It is a true statement.That seems a rather counterintuitive statement. Doesn't the Moon rotating around the Earth imply that that interaction is the dominant force?
Then why is moon not ripped away from Earth...It is a true statement.
If we ignore the Sun and consider the Earth and moon in isolation, the moon clearly orbits the Earth. Both are pulled by the Sun with roughly the same force, so this is a reasonable way of looking at the situation.
But if you plot the path of the moon around the sun, the path is always concave toward the Sun and is not always concave toward the Earth.
Or you could do it the hard way. Look up the mass of the Sun, the mass of the Earth, the sun to earth distance and the sun to moon distance. Do the inverse square calculation and see which is larger.
Edit: I just looked up the relevant figures. The sun wins by a factor of roughly 333,000 on mass. The Earth wins by a factor of roughly 152,000 on r2. Net is a 2 to 1 win for the Sun over the Earth. That matches what I Googled up earlier and what my teachers told me half a century ago.
Both the Earth and the Moon are accelerated towards the Sun at approximately the same rate. They are in "free fall" around the Sun. In such a case, the Earth's gravity keeps the Moon orbiting around it while both of them orbit the Sun.
As already pointed out both the Earth and Moon are being pulled on by the Sun by pretty much the same amount. I say "pretty much" because at Full moon, the Moon is slightly further from the Sun than the Earth is and during the new moon is is slightly closer. This produces a small difference in the gravitational accleration on them caused by the Sun. This has the tendency to "stretch" the Moon's orbit along the Earth-Sun line. This is much like the effect the sun has on Earth's ocean tides, So we can say that the Sun has a tidal effect on the Moon's orbit. Unlike straight gravitational pull, tidal forces fall off by the cube of distance rather than by the square of the distance. (this is why, even though the Moon's gravitational pull on the Earth is much weaker than the Sun's, its tidal effect is larger. It is 1/400 the distance from the Earth than the Sun is.)