If we are standing on earth, then some force (gravity of earth) is pulling us down. Can't we make a force which can oppose gravity? Can't we make an object of zero mass?
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3Just put your laptop on your desk. It is not accelerating downwards. You opposed gravity! Now let your laptop fall on the ground. Now you made it weightless until it hits the ground! – Gonenc May 12 '15 at 16:57
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1possible duplicate of Can gravity be shielded, like electromagnetism? – John Rennie May 12 '15 at 16:59
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1See also Is it theoretically possible to shield gravitational fields or waves?. No, gravity cannot be blocked or shielded so we cannot have an object in a gravitational field that has zero weight (NB zero weight not zero mass). – John Rennie May 12 '15 at 17:01
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@JohnRennie Actually a falling object would do as a zero weight object until it hits the ground. – Gonenc May 12 '15 at 17:05
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@gonenc: yes, true :-) I was of course thinking about an object stationary wrt the ravitational field. – John Rennie May 12 '15 at 17:14
2 Answers
There is a force that is preventing us form falling through the Earth or through the floor of your house. It is called normal force.
It is not possible in this way to make an object of zero mass, because mass isn't dependent on the force: my mass is exactly the same on Mars or Jupiter.

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In our universe, there are only four known forces which are given names such as "Strong", "Weak", "Electromagnetic", and "Gravitation". And, there seems to be an almost continuous report in the news of evidence or rumors of evidence for a 5th force but so far insufficient to be considered seriously.
Of the four known forces, three of them are stronger than gravity. In fact, so much stronger that gravitational forces are ignored entirely during interactions of one or more of the three other forces.
So, yes, there is a normal force that prevents you from falling through the floor. And, this normal force has its origins in the Electromagnetic Force -- that is, the forces generated by charges (static, in motion, and accelerating). Indeed, the Electromagnetic Force is the one responsible for just about everything you can see, feel, touch, lift. Or, let's say everything you encounter, even yourself.
When you fly in an airplane gravity is trying to pull you down to the earth but the Electromagnetic Force displayed in a myriad of ways is keeping you aloft and safely in the air.
You also ask, why we can't make an object of zero mass. Not sure what kind of object you have in mind but I actually do this, in a way, every day of the week. My hobby is amateur "ham" radio and when I transmit I am creating radio waves that have zero rest mass. When my station receiver and antenna system picks up other radio waves of zero rest mass, the electronics of my radio transmute that zero rest mass "thing" into forces that can move and vibrate air molecules (that is, make sound). Yet the only force behind all of this magic is the Electromagnetic Force.

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