Uncertainty principle says that one cannot measure exactly the position and momentum of a particle at same time. As per common understanding when we are measuring momentum of an object it is implicit that we aware of its position. My doubt is in Quantum world, how can we measure momentum of a particle without knowing its position. Are the two momentum and position are mutually exclusive?
I know a "kind of" answer.
A "velocity selector" AKA "Wein filter" will pass particles with a narrow fixed range of velocities. If we know the species (and therefore the mass) we have measured the momentum of all particles passing the filter without measuring position in the direction of travel (but we have measured position transverse to the direction of travel).
The reason this is interesting is that while the Heisenberg principle limits your precision in measuring both $x$ and $p_x$ at the same time it does not limit your precision in measuring $y$ and $p_x$ at the same time.