Water contained in a bucket is whirled in a vertical circle using an attached string. The water does not fall out even when the bucket is inverted at the highest point of its trajectory. From this, we can conclude that in this position,

Step-by-step solution

At the highest point of the vertical circle, the forces acting on the water are its weight mg acting downwards and the normal reaction N exerted by the bottom of the bucket, also acting downwards. The net downward force provides the necessary centripetal force for circular motion: N + mg = mv^2 r For the water not to fall out, it must maintain contact with the bucket, which means the normal reaction N must be greater than or equal to zero, i.e., N 0 . mv^2 r - mg 0 mg mv^2 r This implies that mg is not greater than