A bucket filled with water is tied to a piece of string and whirled in a vertical plane.(I)at which position (x or y) will the bucket be heavier and explain.(II) give a reason why the water does not pour out of x.

1 answer

Well, heavier ?
I think you mean the tension in the string
at the bottom it is m g + m v^2/R
at the top it is m g - m v^2/R
if m v^2/R is greater than m g, the tension remains positive and neither the bucket or the water in it fall.
Of course if v is too small, the bucket will not make it to the top and the water in it will spill.