Let the tension on the wire be #T#
The vertical component of tension (#Tcostheta#) balances the weight of the ball of mass m i.e. #mg#
So #Tcostheta=mg.....[1]#
The horizontal component of tension #Tsintheta# will provide the centripetal force to rotate the ball in a circular path of radius R with angular velocity #omega#
So
#Tsintheta=momega^2R......[2]#
Here #R=0.5+1.2*sintheta=0.5+0.6*sin30=1.1m#
Dividing [2] by [1] we get
#tantheta=(omega^2R)/g#
#=>omega=sqrt((g tantheta)/R)#
#=>omega=sqrt((9.8xx tan30^@)/1.1)#
#=>omega=sqrt(9.8 /(1.1xxsqrt3))=2.27rad"/"s#
