44. A point P on a CNC controlled XY-stage is moved to another point 'Q' using the coordinate system shown in the figure below and rapid positioning command (GOO). 700 600 Y 500 400 300 P(200,300) 200- 100 Q(800,600) UM 100 200 300 400 500 600 700 800 900 X A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screw, each with a uniform pitch of 0.5 mm. The time needed to position the point 'P' to the point 'Q' is minutes (round off to 2 decimal places). 45. A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as 1000 kg/m, and the acceleration due to gravity as 10 m/s, the natural frequency of small oscillations of the ball, normal to the water surface is decimal places). radians/s (round off to 2