Question

universal law of gravitation states that every object exerts a gravitational force of attraction on every other object if this is true why don't we notice that forces why don't the two objects in a room move towards Each Other due to this force

Answer 1

The magnitude of the gravitational force acting on either of two 1 kg masses separated by 1 meter as a result of one another is just 6.67*10^-11 N.
Whereas, the frictional force acting on either mass (assuming them to be made of rubber and resting on concrete) is approximately 10 N.
So the force that restrains their movement (friction) is approximately 150 billion times stronger than the force that could move them (gravity)!

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Answer 2

Sir Isaac Newton first presented his three laws of motion in the "Principia Mathematica Philosophiae Naturalis" in 1686. His third law states that for every action (force) in nature there is an equal and opposite reaction. In other words, if object A exerts a force on object B, then object B also exerts an equal and opposite force on object A. Notice that the forces are exerted on different objects.