Note that no specific angle was mentioned and "uniform motion" was claimed. This indicates to me that the objects weight should be ignored and only the centripetal force component is to be considered.
The angular velocity is 1.28/.34= 3.76 rad/sec thus the tangential velocity = 1.2*3.76= 4.51m/s.
The Fcentripetal = mv2/r = .38*4.512/1.2= 6.45 Newton = Tension