It is said that when force is applied perpendicular to velocity, there is no change in kinetic energy since there is no change in speed. Exactly what happens when there is uniform circular motion. System => object undergoing uniform circular motion.
The only force which is acting is the force causing centripetal acceleration whose direction is at right angle to the direction of the velocity so no work is done on the object by the force causing the centripetal acceleration,
My question is, if a particle moving horizontally with some speed $V_{\rm x}$ and a force acts along $y$-axis . . . . System => the projectile
No force in the horizontal direction, thus no change in the horizontal component of velocity, and a downward gravitational attractive force which does work on the projectile which in turn changes its downward component of velocity had hence its kinetic energy.