When a ball is tied to a rope and spun in a constant circular motion, it experiences a centripetal force that keeps it moving in a curved path. This centripetal force is provided by the tension in the rope, which acts as the inward force required to maintain the circular motion.
Gravity, on the other hand, always acts vertically downward towards the center of the Earth. It is a force that attracts objects with mass towards each other.
When the velocity magnitude of the ball is below a certain point, gravity can still exert a noticeable effect on the ball because the centripetal force provided by the tension in the rope may not be sufficient to fully counteract the force of gravity. In this case, the ball will experience a net downward force, causing it to sag slightly.
However, when the velocity magnitude of the ball increases beyond a certain point, the tension in the rope increases proportionally to provide the necessary centripetal force. At this point, the tension in the rope becomes strong enough to counteract the force of gravity effectively. As a result, the ball does not sag, and the circular motion is maintained without being noticeably affected by gravity.
It's worth noting that the tension in the rope must be adjusted appropriately to balance the centripetal force and gravity for a given velocity. If the tension is too low, the ball will sag more due to the dominant effect of gravity. If the tension is too high, it may exceed the breaking strength of the rope or cause the ball to move in an elliptical or spiral path rather than a circular one.