A60 cm rope is tied to the handle of a bucket which is then whirled in a vertical circle.

the complete question in the attached figure

a) we know that
T - mg = mv^2/r
The net forces equal the mass times the centripetal acceleration
 So
T=50 N
m=3 kg
r=0.60 m
v = sqrt((T-mg)r/m) = sqrt((50-(3*9.8))*(.60)/3) = 2.03 m/s 

the answer part a) is  2.03 m/s 

b) At the top the equation becomes T+mg=mv^2/r
but here the critical speed occurs when T = 0
so the critical speed is v = sqrt(rg) = sqrt (.60*9.80) = 2.42 m/s

the answer part b) is 2.42 m/s