why do objects fall towards centre of gravity of earth only...???
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It is also true that a free falling (no air resistance) object falls with an acceleration of 9.8 m/s2—but it's still just the gravitational field. It doesn't matter what object you put near the surface of the Earth, the gravitational field due to the Earth is constant and pointing towards the center of the Earth.
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Gravity works by pulling objects towards something with mass. Because of this, we feel we are pulled toward the center of the Earth. So you would fall towards the center of the Earth, but once you pass the center, you would then slow down and start "falling" in the opposite direction, back towards the center again.
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